Science topic

Schrodinger - Science topic

Explore the latest questions and answers in Schrodinger, and find Schrodinger experts.
Questions related to Schrodinger
  • asked a question related to Schrodinger
Question
4 answers
Is useless quantum mechanics inherent in Schrödinger's PDE?
It is well known that the Schrodinger PDE SE in 3D geometric space plus time as an external controller is incomplete and any attempt to combine it with unitary 4D space such as special and general relativity would be useless.
The success of the SE is solely due to its statistical nature and not to its current formulation.
We assume that knowing this fact, we can know in advance in which physical situation the current SE can work effectively and in which other it would remain dead, despite the denial of the brainwashed iron guards.
The question arises, is it possible to reformulate SE?
Relevant answer
Answer
Its not usless, only not always understandable.
  • asked a question related to Schrodinger
Question
3 answers
I'm performing protein-protein interactions using a Piper-docked pose and later Desmond, but I'm not seeing the expected residue interactions in the Desmond molecular dynamics (MD) simulation. Any insights?
Relevant answer
Answer
Using Piper and Desmond for protein-protein interaction analysis involves several steps, from docking to molecular dynamics simulations. Here’s a brief overview of the process and some insights that might help you troubleshoot the lack of expected residue interactions in Desmond’s MD simulation:
1. Protein Preparation:
  • Ensure that both proteins are properly prepared before docking. This includes protonation, assigning correct bond orders, and adding missing hydrogens.
2. Docking with Piper:
  • Setup: Define the receptor and ligand (or in this case, the two proteins interacting).
  • Docking: Run the docking protocol in Piper. You may want to explore different docking strategies and scoring functions to optimize the pose.
  • Analysis: After docking, analyze the results to select the best pose(s) based on the docking score and any other criteria you have.
3. Preparing for MD with Desmond:
  • Setup: Import the docked complex into Desmond. Ensure the complex is correctly oriented and that any necessary counterions are added for charge neutrality.
  • System Building: Build the solvent environment around the complex, and then parameterize the system with the appropriate force field.
  • Energy Minimization: Perform energy minimization to remove any steric clashes or high-energy conformations that may have arisen during the setup.
4. MD Simulation:
  • Equilibration: Run an equilibration phase to allow the system to relax into a stable state. This usually involves gradually heating the system and then applying pressure restraints.
  • Production Run: Conduct the production MD simulation under the desired conditions (temperature, pressure, etc.).
5. Analysis:
  • Trajectory Analysis: After the simulation, analyze the trajectory to identify and characterize protein-protein interactions.
Insights for Expected Residue Interactions:
If you’re not seeing the expected residue interactions, consider the following:
  • Docking Pose: Ensure the docking pose is accurate. Sometimes, the top scoring pose from docking may not represent the biologically relevant conformation. Try analyzing multiple top poses.
  • Force Field and Parameters: Check that the force field and parameters used in Desmond are appropriate for the system you’re studying. Mismatches can lead to incorrect behavior.
  • Simulation Time: The MD simulation might not have run long enough to observe the expected interactions. Proteins can take time to relax into their interacting conformations.
  • Analysis Method: Make sure you’re using the correct method to analyze the MD trajectory. For protein-protein interactions, this might involve calculating distances, angles, hydrogen bonds, or other interaction types.
  • Trajectory Sampling: The simulation might not be sampling the relevant regions of conformational space. You may need to run longer simulations or use enhanced sampling methods.
  • Starting Structure: The structure you started with might have had some intrinsic strain or wasn’t the most stable form of the complex. Re-evaluate the starting structure if necessary.
Troubleshooting Steps:
  1. Re-evaluate the Docking Pose: Look at other high-scoring poses or re-run the docking with different parameters.
  2. Increase Simulation Time: Run a longer simulation to allow more time for the proteins to interact.
  3. Adjust Analysis Parameters: Make sure the criteria for defining interactions are not too strict or too lenient.
  4. Temperature and Pressure: Ensure that the simulation conditions are physiological. Extreme conditions can alter protein behavior.
  5. Counterions and Solvation: Check that the system is properly solvated and that the ionic strength is correct.
If after these checks you still do not see the expected interactions, it may be necessary to revisit the experimental data supporting those expected interactions or consider additional computational or experimental approaches to validate your findings.
  • asked a question related to Schrodinger
Question
3 answers
Hello, can anyone please tell me how to setup GPU to run MD simulations in Schrodinger Maestro in Windows 11? My laptop is running Windows 11 and I want to do MD simulations but when I try to run it, it says dummy GPU, No GPU has been found. Please can anyone tell me an easy way to solve this problem? I am not an expert in computers. Thanks
Relevant answer
Answer
it is not possible to set up GPU acceleration for Schrödinger Maestro MD simulations on Windows 11. Schrödinger's GPU-accelerated molecular dynamics simulations, including those run through Desmond, are only supported on Linux operating systems. For Windows users, the recommended approach is to run Maestro locally on your Windows machine for visualization and job setup, but submit computationally intensive tasks like MD simulations to a Linux-based computing cluster or cloud service that has the necessary GPU hardware and software configuration.
  • asked a question related to Schrodinger
Question
20 answers
If ever confirmed, the applicative potential would be tremendous...
I refer here to Grinwald's publication:
from which I quote below:
"Ultimate dependence on truths of pure numbers, rather than pre-existing physical law, would seem a desirable step towards a more reasoned description of quantum mechanics, which is empirically correct but appears deeply mysterious."
"A standard teaching is that the wavefunction evolves deterministically under Schrödinger’s equation, until the moment of measurement when it undergoes “collapse” according to the Born probabilities. However the central limit theorem implies a random process underlying the Schrödinger equation itself, counter to the essentially deterministic view of the wavefunction."
"More precisely, it is concluded that the content of Schrödinger’s equation is equivalent to propagation by a generalized Gaussian function, normalized in the sense of C [i.e. complex number system] with the norm conserved in time. The key role of the Gaussian is attributed to the central limit theorem, which extends to random vectors in infinite-dimensional separable complex Hilbert spaces."
"The change from interpreting quantum mechanics to reconstructions of it has been described by Grinbaum [...] as a paradigm shift. All the reconstructions rest on assumptions. Arguably the present assumptions are few in number, of a general nature and relatively simple: they consist of a Gaussian propagator, and norm conservation in C.
Randomness has been seen as a puzzle to which the many worlds interpretation [...] may provide a resolution. As the present treatment deals with Gaussian functions, which occur by virtue of the central limit theorem, randomness is implied, but it is indifferent as to possible sources of randomness."
I appeal here to physicists in a spirit of free and friendly discussion.
Relevant answer
Answer
I'm following up on Juan Weisz's informative post dated February 07, 2023.
Among the various formulations of Classical Mechanics, the nearest one to the Schrödinger version of Quantum Mechanics is based on the classical (dispersive) Hamilton–Jacobi Equation. Refer to :
  • M.F. Girard, “The Quantum Hamilton-Jacobi Equation and the Link Between Classical and Quantum Mechanics”, 2022 - https://arxiv.org/abs/2203.07005
  • M.F. Girard, “Evaluation of the Feynman Propagator by means of the Quantum Hamilton-Jacobi Equation”, 2023 - https://arxiv.org/abs/2210.02185
Local smoothing properties of dispersive equations, including the Schrödinger equation, were highlighted by Constantin et al. :
Darbon et al. recently made connections between Hamilton–Jacobi partial differential equations and a broad class of Bayesian posterior mean estimators with Gaussian data fidelity term and log-concave prior relevant to image denoising problems. Follow:
  • Darbon et al., “On Bayesian Posterior Mean Estimators in Imaging Sciences and Hamilton-Jacobi Partial Differential Equations”, 2020 - https://arxiv.org/pdf/2003.05572
  • asked a question related to Schrodinger
Question
3 answers
Could you please advise on how to perform molecular docking for polysaccharides (large molecules)? I have previously used Glide in Schrödinger for small molecule docking, but what would be the most appropriate software or approach for handling polysaccharides?
Could you provide any further guidance or recommendations on this matter?
Relevant answer
Answer
Molecular docking of polysaccharides, which are large, complex carbohydrates, presents unique challenges compared to small molecules due to their size, flexibility, and the presence of multiple hydroxyl groups that can participate in hydrogen bonding. Here’s a general approach and some software recommendations for performing molecular docking with polysaccharides:
Software Recommendations:
  1. GROMACS with HADDOCK: HADDOCK is a software for macromolecular docking, and it can be used in conjunction with GROMACS for molecular dynamics simulations. It is capable of handling large and flexible molecules like polysaccharides.
  2. Rosetta: Rosetta is a suite of software for macromolecular modeling, which includes a protocol for carbohydrate docking called CARDS (Carbohydrate Docking with Rosetta and Dynamics). It is specifically designed for the modeling of carbohydrates and their interactions.
  3. AutoDock: Although primarily used for small molecules, AutoDock can be used for larger molecules if you have a powerful enough computer. The newer version, AutoDock4, has some capabilities for handling larger ligands.
  4. MOE (Molecular Operating Environment): MOE has tools for handling large and flexible molecules and can be used for docking polysaccharides to proteins.
  5. CHARMM: CHARMM is a comprehensive molecular modeling package that can be used for simulating and analyzing biological macromolecules, including carbohydrates.
Approach for Docking Polysaccharides:
  1. Preparation of Polysaccharide Structure:Use software like CHARMM, GlycanBuilder, or other carbohydrate modeling tools to build the 3D structure of the polysaccharide. Perform energy minimization and molecular dynamics simulations to refine the structure and account for flexibility.
  2. Receptor Preparation:The protein or receptor target should be prepared in a similar way to small molecule docking: protonation, energy minimization, and removal of any unnecessary solvent molecules or crystallographic waters.
  3. Docking:Define the binding site on the receptor where the polysaccharide is expected to bind. Use the chosen software to perform the docking. With software like HADDOCK or Rosetta, you can use information from experiments (e.g., NMR or X-ray crystallography data) to guide the docking process. Account for the flexibility of both the polysaccharide and the receptor. This might involve sampling different conformations of the polysaccharide and using ensemble docking techniques.
  4. Scoring and Selection:Evaluate the docked poses using appropriate scoring functions. For polysaccharides, scoring functions that include terms for hydrogen bonding and van der Waals interactions will be particularly important. Select the best-scored poses for further analysis.
  5. Post-Docking Analysis:Perform molecular dynamics simulations on the docked complexes to assess their stability and to refine the binding mode. Analyze the interactions between the polysaccharide and the receptor using tools like MDAnalysis or PyMOL.
Additional Recommendations:
  • Parameterization: Ensure that the force fields and parameters used in your simulations are suitable for carbohydrates.
  • Computational Resources: Docking polysaccharides is computationally intensive. Make sure you have access to sufficient computational resources.
  • Validation: Validate your docking approach with known structures of carbohydrate-protein complexes if available.
  • Expertise: The process of docking large, flexible molecules like polysaccharides often requires a deep understanding of both the software and the biological system. Collaboration with experts in computational biology or bioinformatics can be beneficial.
Keep in mind that molecular docking is a complex process with many variables, and it often requires iterative refinement and validation to obtain reliable results.
  • asked a question related to Schrodinger
Question
3 answers
As I understand it, the folding energy of a protein is usually expressed as a negative value. ΔG < 0 is expected for maintaining the native state in the folding condition.
However, when calculating protein energy with FoldX, positive values appear, as shown in the screenshot below.
This has led to significant confusion regarding whether a mutation can be more stable compared to the wild type.
For instance, if the ΔG (WT) = 30 kcal/mol and ΔG (Mut) = 40 kcal/mol using FoldX, is ΔΔG = 10 kcal/mol or -10 kcal/mol?
Is a negative ΔΔG value indicative of greater stability?
Moreover, when using Schrödinger software, energy values are expressed as negative. For instance, Schrödinger gives ΔG(WT) = -18693.8 kcal/mol and ΔG(Mut) = -18712.4 kcal/mol. In this case, what should be subtracted from what?
There is also confusion due to different literature sources stating ΔΔG = ΔG(WT) - ΔG(Mut) or ΔΔG = ΔG(Mut) - ΔG(WT). Which is correct?
Please provide clarification.
Relevant answer
Answer
The confusion regarding the sign of the stability values when using FoldX or other computational biology software tools is understandable, as different programs may use different conventions for reporting energy values.
FoldX and Positive Values:
FoldX typically reports the stability of a protein in terms of the energy required to unfold it, which can be positive. This is because FoldX calculates the energetic changes in the protein structure, and a positive value indicates that energy is required to disrupt the protein’s structure. In FoldX, a higher positive value means the protein is less stable because more energy is required to unfold it.
ΔΔG Calculation:
When you’re comparing a wild-type protein to a mutant, the change in stability (ΔΔG) is calculated as the difference in the energy between the two states. The convention used in FoldX is:
ΔΔG = ΔG(Mut) - ΔG(WT)
This means if ΔG(WT) = 30 kcal/mol and ΔG(Mut) = 40 kcal/mol using FoldX, then ΔΔG = 40 - 30 = 10 kcal/mol. A positive ΔΔG value in FoldX indicates that the mutation has destabilized the protein compared to the wild type. Conversely, a negative ΔΔG value would indicate increased stability of the mutant compared to the wild type.
Schrödinger Software and Negative Values:
In contrast, Schrödinger and some other software tools use the convention where a more negative ΔG value indicates a more stable protein. In Schrödinger’s case, if ΔG(WT) = -18693.8 kcal/mol and ΔG(Mut) = -18712.4 kcal/mol, the ΔΔG would be calculated as:
ΔΔG = ΔG(WT) - ΔG(Mut) ΔΔG = -18693.8 - (-18712.4) = -18712.4 + 18693.8 = -18.6 kcal/mol
Here, a negative ΔΔG value indicates that the mutation has made the protein more stable, which aligns with the general thermodynamic principle that a more stable state has a lower free energy.
Conclusion on ΔΔG:
The correct formula for ΔΔG depends on the convention used by the software you are using:
For FoldX and similar tools that use positive values: ΔΔG = ΔG(Mut) - ΔG(WT)
For Schrödinger and similar tools that use negative values: ΔΔG = ΔG(WT) - ΔG(Mut)
When interpreting results, always refer to the software’s documentation or conventions to understand how stability is reported. Remember that the key is the change in stability (ΔΔG), not the absolute values of ΔG(WT) or ΔG(Mut).
  • asked a question related to Schrodinger
Question
2 answers
Although Quantum Entanglement Phenomenon was coined by Schrodinger in 1935 but this phenomenon was described by Maharaj
Saheb Pandit Brahm Sankar Misra, M. A. (1861-1907) at least 25 years before Schrodinger contemplated this phenomenon. In His book Discourses on Radhasoami Faith, First Edition brought out in 1909, He writes: "It would not therefore be unjustifiable for us further to infer that the spirit -force, like the other forces of nature, partakes of the influences of its original source, and that whenever it converges and forms its focus, the conditions brought about are, to some extent, similar to those present in the original source, the similarity being complete when the converging lens or mirror does not introduce an element of obstruction. In the physical universe, such a complete likeness is very rarely met with".(Article 16-Spirit And Its Source)
Relevant answer
Answer
Yes, I am sure. Quantum Entanglement is regardless of distance between the particles.
  • asked a question related to Schrodinger
Question
4 answers
I have conducted virtual screening using Schrödinger on a database of 17,000 molecules. Unfortunately, I cannot use the system with the Schrödinger license at the moment. I am trying to find a way to extract the binding energy from the PoseViewer .pv.maegz file generated by the screening on my local computer without using Schrödinger.
I attempted to convert the .maegz file to .sdf and then extract the binding energy, but this approach did not work. I would greatly appreciate any guidance or suggestions from those who have encountered and resolved a similar issue.
Relevant answer
Answer
Hi Nilanjana Mani , have you tried looking into the csv file that docking generates? It might have your energy values in tabulated format.
  • asked a question related to Schrodinger
Question
4 answers
We assume that we can find a statistical matrix mechanics equivalent to Schrödinger's PDE in two consecutive steps:
i-Transform the Schrödinger PDE describing the wave function Ψ into its square describing Ψ^2=Ψ. Ψ*.
Strikingly, the Schrödinger PDE describing Ψ^2, when supplemented by the natural laws of vacuum dynamics, is more complete than the classical Schrödinger PDE itself.
ii-Use the transition-B-matrix statistical chains to find the required equivalence for the PDE of Ψ^2 (in the same way as that for the PDE of thermal diffusion) and therefore its solution for different internal (spontaneous) potentials ) or external.
Note that the well-known Heisenberg matrix mechanics is neither statistical nor complete.
Relevant answer
Answer
Science leaves the era of mathematics and enters the era of matrix mechanics and the turning point is the discovery of numerical statistical theory called Cairo techniques and its transition matrices eligible to solve almost all problems of classical physics and of quantum mechanics.
No more partial differential equations, no more numerical integration, no more FDM techniques. . etc.
Statistical matrix mechanics is capable of solving all of the above problems and additionally predicting unknown universal physical rules.
Note that the Heisenberg matrix and the Dirac matrix are neither physical nor statistical and incomplete.
  • asked a question related to Schrodinger
Question
11 answers
We assume that the Schrödinger wave equation,
iℏ(dψ/dt)= Ĥψ. . . . . (1)
is incomplete and cannot be considered a unified field theory.
on the other hand, its square,
d/dt)partial U= D Nabla^2 U+ S. . . . (2)
Where U=Ψ^2=Ψ . Ψ*
and S is the source/sink term (extrinsic or intrinsic).
is more complete and more eligible to be a unified field theory.
Over the past four years, Equation 2 has been successfully applied to solve almost all classical physics situations such as Poisson and Laplace PDE, heat diffusion equation, and quantum physics problems such as quantum particles in a well of infinite potential or in a central field.
Additionally, Equation 2 has also been shown to be effective in solving pure mathematical problems such as numerical differentiation and integration as well as the sum of infinite integer series.
Finally, Equation 2 was applied to shed light on the mystery of the formation and explosion of the Big Bang.
Relevant answer
Answer
It is easy to show that unified field theory belongs to the square of the Schrödinger wave equation rather than to the classical Schrödinger wave equation itself.
You first transform the Schrödinger PDE describing the wave function Ψ into another describing its square Ψ^2=Ψ. Ψ*. Strikingly, the modified Schrödinger PDE describing Ψ^2, when supplemented by the natural laws of vacuum dynamics, is more complete than the classical Schrödinger PDE itself.
The reformulated Schrödinger partial differential equation lives and operates in the 4D unit space and therefore belongs to the chains of the B matrix which is a product of the statistical method called Cairo techniques.
You can take a particular approach to show that unified field theory belongs to the square of the Schrödinger wave equation rather than the classical Schrödinger wave equation itself.
This particular approach focuses on applying B-matrix chain techniques to answer three fundamental questions that continually challenge the classic Schrödinger equation:
A-Can we replace Schrödinger's partial differential equation with a kind of statistical matrix mechanics capable of describing the formation and explosion of the Big Bang?
B-Can we deduce an expression for the reverberation time in audio rooms?
C-Is it possible to calculate a finite numerical integration via matrix mechanics?
Mathematicians and theoretical physicists with the greatest skills in the classical Schrödinger equation cannot answer these particular questions even in their dreams.
Finally, we present a correct and exact answer to the three questions A, B and C [1] proving that the unification of field theory is the square of the Schrödinger wave equation sublimated by the rules of vacuum dynamics .
1-Is unified field theory Schrödinger's wave equation or its square? A unitary spatio-temporal vision, ResearchGate, IJISRT journal, July 2024.
  • asked a question related to Schrodinger
Question
9 answers
We assume that there is a physico-statistical meaning to the constant π other than circular geometry, but the iron guardians of the Schrödinger equation deny this.
The iron guardians of the Schrödinger equation are brainwashed and mistakenly believe that the Schrödinger equation is considered a unified field theory, implying that any equation not in it is false.
The strings of matrix B, the product of the Cairo techniques procedure, predict that the time dependence of the heat equation or the sound intensity equation is expressed as follows:
dU /dt =-U.Const.2π.Area/Volume . . . (1)
for any geometric object.
Note that equation 1 implies the following rule:
3D bodies of different shapes cannot have the same volume-to-surface ratio unless they have exactly the same volume and surface area [ResearchGate Q/A 6-6-2023].
Relevant answer
Answer
Reference 1 is not a publication at all.
Reference 2:
1) It's an SCIRP publication. SCIRP's academic integrity is under severe doubts so I would not rate that very serious.
2) If you look into it, you see that the author modifies the Scrödinger equation, so it does not support your claim.
3) It also writes about general relativity which is not part of the Schrödinger equation.
  • asked a question related to Schrodinger
Question
4 answers
The short answer is yes.
Scientific education in the West throughout the 20th century was based on the assumption that Schrödinger's PDE is the only unified theory of energy fields (microscopic and macroscopic), which is false.
Schrödinger's PDE is fundamentally incomplete because it lives and operates in 3D geometric space plus real time as an external controller.
Our mother nature lives and functions in a unitary 4D x-t space with time as a dimensionless integer woven into geometric space.
We assume that a serious improvement in scientific teaching and research can be achieved by describing the 4D x-t unit space via a 4D statistical mechanics unit space or any other adequate representation.
Relevant answer
Answer
The Schrödinger Equation is right and our current Mathematics is incomplete.
The differentiation of discontinuous functions exist and is easy, to any order. See it online.
New solutions open to the Schrödinger equation with that, while keeping the old ones.
We live in 6D but a 3D slice is accurate when comoving. Then, mass represents the amount of matter. Even in 3D mass can be transported by massless particles -- even when they are isolated. One photon can recoil an atom.
  • asked a question related to Schrodinger
Question
4 answers
Doing a Google search brings up the statement (Schrödinger's equation and the duality diffusion equations are equivalent. In turn, Schrödinger's 1931 conjecture is solved.).
The above statement is absolutely false.
The heat diffusion equation lives and operates in real measurable space-time while the Schrödinger equation lives and operates in imaginary space-time.
Furthermore, the Schrödinger equation itself is incomplete because it ignores median symmetry, boundary conditions and the principle of least action. . etc.
Relevant answer
Answer
The Schrödinger equation, like the diffusion equation, follows from first principles.
  • asked a question related to Schrodinger
Question
2 answers
The short answer is yes.
The Schrödinger equation is over 100 years old and, what's more, it was born incomplete.
In 2020, a new numerical statistical theory called Cairo Techniques emerged that challenges the classical theory of the Schrödinger equation across all scientific fields, including its own castle of quantum mechanics.
We predict that in the next ten years, most scientific research will escape the Schrödinger equation and focus on the new statistical theory.
Relevant answer
Answer
This is just a short answer to shed some light on the question and its answer, and thanks to the Spanish contributor for his helpful answer.
His answer contains too much discussion, which I want to answer in separate paragraphs as follows:
1-Heisenberg QM was stillborn because it is incomplete because it lives and works in 3D geometric space in real time t as an external controller.
2-In 2020, a new theory of numerical statistical mechanics was born in matrix form.
It is a complete theory because it lives and works in 4-D unitary x-t space.
The real time t disappears completely and is replaced by a discrete integer Ndt, where N is the number of iterations and dt is the time jump.
This is the so-called Cairo technique.
This new matrix theory is the only physical transition matrix known to us and was successfully applied to solve almost all physical and mathematical problems (heat diffusion, QM problems, sound intensity in sound rooms, mathematical integration and differentiation, sum of infinite integer power series..etc..)
This is what we call Rise of Matrix Mechanics.
3- Probability and statistics are missing from mathematics and theoretical physics.
The classical definition of probability as the number of successful trials divided by the total number of trials is naive, and the quantum definition of probability will make you laugh.
We hypothesize that one of the reasons why this new matrix theory has been widely successful is that it provides the only correct definition of probability.
Finally, we believe that the classical Schrodinger equation faces fatal problems due to the fatal challenge of new statistical theory.
In the next ten years, we expect the number of scientific studies based on statistical theories to grow enormously at the expense of the classical Schrodinger equation.
  • asked a question related to Schrodinger
Question
2 answers
It's both.
Relevant answer
Answer
Hello,
Schrödinger's equation can be considered as a diffusion equation with a diffusion coefficient β 2 = ℏ / 2 m.
he Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics.
Thanks,
  • asked a question related to Schrodinger
Question
4 answers
The short answer is yes, it is absolutely true.
We first affirm that the matrix mechanics of W. Heisenberg, Max Born and P. Gordon (H-B-G) was born dead and destroyed by the Schrödinger equation in three years.
This is not surprising since the HBG matrix is ​​designed to resolve energy levels in the hydrogen atom and is therefore only a subset of SE PDE.
On the other hand, modern statistical mechanics (B matrix chains and Cairo techniques in 2020) has established itself as a giant capable of solving almost all physics and mathematics problems.
Here we can say that it is a unified field theory and Schrödinger's PDE is one of its subsets and not vice versa.
We predict that future scientific research over the next ten years will increasingly focus on the area of ​​modern matrix mechanics, at the cost of eliminating the Schrödinger equation.
Relevant answer
Answer
This is just a brief answer which aims on the one hand to clarify the question and its answer and on the other hand to thank our fellow contributors for their helpful answers.
It is true that extraordinary allegations require extraordinary evidence.
Unlike the Schrödinger equation and its derivatives, B matrix chains and Cairo statistical techniques are capable of numerically solving almost all energy fields [1,2,3,4,5] of quantum physics and from classical physics like the Poisson and Laplace PDE, heat diffusion equation, sound intensity in audio rooms in addition to pure mathematical problems such as differentiation and integration.
We assume that this makes it a unified field theory.
The references:
1-An efficient reformulation of Schrödinger's partial differential equation
Full text available
May 2024, Researchgate, IJISRT journal.
2-Is it time to reformulate the Poisson and Laplace partial differential equations?
Article
Full text available
June 2023, Researchgate, IJISRT journal.
3-A statistical numerical solution for the time-dependent 3D heat diffusion problem without the need for the PD heat equation or its FDM techniques.
Full text available
July 2021, Researchgate, IJISRT journal.
4-Theory and design of audio rooms -A statistical view, Full text available
July 2023, Researchgate, IJISRT journal.
4-Effective unconventional approach to statistical differentiation and statistical integration
Full text available
November 2022, Researchgate, IJISRT journal.
  • asked a question related to Schrodinger
Question
4 answers
We assume that V(x,y,z,t) is the external potential applied to the quantum particle enclosed in a closed system.
What is quite surprising is that there exists another spontaneous component for V which comes from the energy density of the system itself expressed by,
V(x, y, z, t)=Cons U(x, y ,z ,t) . . . . (1)
Eq 1 is a revolutionary breakthrough.
Equation 1 means that quantum energy can be transformed into quantum particles and vice versa.
Additionally, Equation 1 (predicted by the B-matrix chains of the Cairo Statistical Numerical Method) eliminates any confusion about whether the Schrödinger PDE is a wave equation or a diffusion equation and provides a definitive answer:
she could be both.
Relevant answer
Answer
Answer II-Continued
The death of critical thinking will kill us long before AI. (Joan Westenberg)
This is just a brief response to shed some light on the question and its answer and to thank our Argentinian friend for his helpful response.
Schrödinger's PDE,
i h dΨ/dt)partial=h^2 . Nabla^2 Ψ/2m + V Ψ . . . . (1)
is precise but incomplete.
Now think about solving SE for Ψ^2 and not Ψ.
Equation 1 transforms to,
dΨ^2/dt)partial=C1. Nabla^2 Ψ/2m + C2 .V . . . . (2)
With the following hypotheses proven numerically,
i-Ψ^2=Ψ . Ψ*
ii-Ψ^2 is exactly equal to the quantum energy density of the quantum particle.
iii-Ψ^2 is exactly equal to the probability of finding the quantum particle in the 4D unit volume element x-t "dx dy dz dt"
iv-Real time t is completely lost and replaced by the dimensionless integer N dt.
Where N is the number of iterations or repetitions and dt is the time jump.
Equation 2 belongs to and is solved by matrix mechanics.
Equation 2 does not need any PDE or FDM method to be solved.
What is quite surprising is that equation 2 is more informative than equation 1.
To be continued.
  • asked a question related to Schrodinger
Question
7 answers
Schrödinger's PDE is too old (+100 years) and fundamentally incomplete but it has proven itself in almost all scientific fields.
He can't die or be fired all at once, at least in the next ten years.
However, in the long term, it is very likely that they will gradually disappear and be replaced by elegant and brilliant theories of modern statistical mechanics.
Relevant answer
Answer
Answer V (continued)
Once again, nature is beautiful and powerful.
It is capable of solving all its mathematics or physics problems in the simplest and fastest ways, and the 4D x-t Matrix B series solution is equally beautiful and wireframed.
In particular, probabilities and statistics that are well defined in the four-dimensional unit space of matrix strings B but belong to a missing part of classical theoretical mathematics and physics are the underlying reason for the superiority of the former.
The following example is a nice explanation of the power of solving the transition series of matrix B to find the sum of infinite algebraic series, which clearly exceeds the power of the Schrödinger equation or one of its derivatives.
Here we consider the statistical-physical solution to a purely mathematical formula.
given by,
Consider the physical statistical solution to a purely mathematical formula.
The question  given by:
Using matrix algebra,[3] how can we show that the series of infinite integers
[(1+x)/2]^N is equal to (1+x)/(1-x), ∀x∈[0,1 [?
We assume that all mathematicians and physicists know that mathematics is the language of physics. However, not all mathematicians and physicists admit that modern physics (classical physics supplemented by B-matrix strings) can be the language of mathematics and replace it in certain areas/situations, as in the case of this question.
A numerical example for validation, the sum of the entire series, 0.99 + 0.99^2 + 0.99^3 + . . . . +0.99^Ntends to 190 as N tends to infinity. The proof of this question is based on the transfer matrix D :
plus the following rule (principle 1) [14].[For positive symmetric physical power matrices, the sum of their eigenvalues ​​is equal to the eigenvalue of their sum of power series] The question arises whether a classical mathematical proof can also be found?
We assume that the proposed axiom or mathematical principle:
[For the real statistical transition matrices that follow,
D(N)= B+B^2+B^3 + . +B^N
the sum of their eigenvalues ​​(λ +λ^ 2 + λ^3+ . . ., where λ∈[0,1[) is equal to the eigenvalue of their sum of integer series (i.e. λ of D(N) ] .. ..Principle (1)
It is obvious that λ is the eigenvalue of the transition matrix B and λ^2 is the eigenvalue of the matrix B^2. . etc.
Note that principle (1) is true and can be validated by numerical calculation.
However, to our knowledge, there is no rigorous mathematical proof of principle (1).
Additionally, using matrix algebra and principle 1, you can prove some mathematical formulas such as:
i- the infinite power series [(1+x)/2]^N is equal to (1+x)/(1-x), ∀x∈[0,1[.
ii- Moreover, the infinite integer series [(1 + Mx) / (1 + M)] ^ N is equal to (1 + Mx) / M (1-x), ∀x element of [0, 1[ and M is a positive integer?
The five examples above show beyond doubt that Schrödinger PDE is a subset of statistical matrix mechanics and not the other way around.
Statistical matrix mechanics is concerned with the nature of quantum particles and their associated energy density, but Schrödinger's PDE describes the probability distribution of the energy density of a quantum system over possible energy levels.
This means that Schrödinger PDE and statistical matrix mechanics are apparently two different subjects. However, Schrödinger's PDE remains a subset of statistical matrix mechanics, in the sense that any solution for the energy density in a quantum system found by Schrödinger's PDE can also be obtained via appropriate statistical matrix mechanics. And more via many missing physical and mathematical solutions in Schrödinger's PDE are well defined and explained in statistical matrix mechanics.
3-Using matrix algebra, how to show that the infinite integer series [(1+x)/2]^N is equal to (1+x)/(1-x), ∀x∈[0,1[ ? , Researchgate, IJISRT journal, November 2023.
To be continued.
  • asked a question related to Schrodinger
Question
5 answers
It’s true that they were published everywhere as clear as the sun.
But who are the old iron guards and why do they defend the Schrödinger equation like its slaves?
The old iron guards are defined as those scientists who are brainwashed and defend their master until their last breath because they wrongly believe that SE and its derivatives are the only unified field theory?
They expect Bohr, Schrödinger, Heisenberg, Dirac, etc. come back from eternity to solve all the mysteries and paradoxes.
As simple as that!
Relevant answer
Answer
Well If I don't mistake Erwin Schrödinger himself worked on developing a unified field theory in the years after his groundbreaking work on quantum mechanics and the wave equation that bears his name. However, his attempts at unification in the 1940s, done in correspondence with Einstein, failed to gain traction. After announcing a result called "Affine Field Theory" in 1947 that was criticized by Einstein as preliminary, Schrödinger gave up his unification efforts.
While some other physicists like Marie-Antoinette Tonnelat and Mendel Sachs worked on unified field theories in the mid-20th century, skepticism from Einstein and others, along with the challenges of uniting quantum mechanics and general relativity, led to progressively fewer scientists focusing on classical unification from the 1930s onward.
The Schrödinger equation remains a cornerstone of quantum mechanics because it has proven incredibly successful at predicting and explaining the behavior of particles at small scales, even if interpretations of what it means about the nature of reality are still debated. There is no evidence that scientists are "brainwashed" into "defending" it - rather, they recognize its continued empirical success.
So the philosophical implications of quantum mechanics, the measurement problem, and how to unify it with gravity remain open questions, claims of a suppressed unified theory are not substantiated. Unification remains an ongoing quest, with theories like string theory and loop quantum gravity representing current approaches, but a fully successful theory has yet to emerge and gain widespread acceptance. Science progresses through evidence and scholarly discourse, not conspiratorial suppression of published theories by "iron guards." Extraordinary claims require extraordinary evidence I suppose.
  • asked a question related to Schrodinger
Question
5 answers
We assume the answer is yes.
Furthermore, this is to be expected to occur in the heat diffusion equation and Schrödinger's PDE from a physical and mathematical point of view.
The question arises: does their combination simplify or complicate the solution?
Relevant answer
Answer
This is just a brief response to shed some light on the question and its answer and to thank our fellow contributors for their helpful answers.
We agree with the revealing response of our fellow professor from Bask-Spain.
The linear combination of these two conditions at a boundary exists but little mentioned (Robin boundary condition) and is expressed mathematically as:
a f + b df/dx=c, where f is the function of interest and a,b,c are 3 constants
It's clear that,
i-if a/b tends towards 0, we recover Neumann
ii-if b/a tends towards 0, we recover Dirichlet
iii-when c = 0, in the context of the diffusion equation, this can be interpreted as a partially absorbing/partially reflecting boundary where particles are both reflected and absorbed onto the assigned contact boundaries with some probability.
For diffusion, in certain geometries, the analytical expression in the form of an infinite series can be obtained by spectral decomposition of the Laplace operator, and the results are, in a way, more "complicated" than the solution of Dirichlet or of Neumann. This more “complicated” solution describes a more general phenomenon which also contains solutions for the Dirichlet and Neumann boundary conditions as limiting cases.
However, we assume that Bmatrix chain techniques can find solutions for the combined Dirichlet and Neumann boundary conditions, which is as simple as a solution for Dirichlet or Neumann alone.
  • asked a question related to Schrodinger
Question
3 answers
I'm struggling to download Maestro by Schrodinger for my small molecule drug discovery, if anyone has the zip file with license key please help me downloading it. Or If there is any other way to download it?
Relevant answer
Answer
Pls, can you name examples of Open source software. I experiencing the same issue since the past three months
  • asked a question related to Schrodinger
Question
2 answers
i have performed simulation in two steps and I wasn't able to merge the energy files. Provide help
Relevant answer
Answer
Can you provide me the script?
  • asked a question related to Schrodinger
Question
1 answer
The short answer is yes.
We assume that the original Schrödinger PDE was introduced for an isolated and bounded quantum system (microscopic or macroscopic) in infinite free space (-∞ <x< +∞).
Meaning Ψ-∞=Ψ+∞ =0 which implies, in some way, the spatial symmetry of the solution.
Relevant answer
Answer
In classical mechanics, where the solution is stimulated or forced via boundary conditions and/or a source term (BC and S), the solution can be symmetric or not depending on the presence of symmetry in BC and/or S.
On the other hand, in quantum mechanical problems where there is neither BC nor S, the solution is completely spontaneous and the symmetry of the solution is essential.
It is worth mentioning that in quantum mechanics there is a connection between symmetries and conservation laws.
Many physicists and mathematicians believe that quantum mechanics explains why Newton's laws of motion are good enough for classical and quantum mechanics.
Additionally, Newton's third law states that for every action, there is an equal and opposite reaction which can be translated into space-time symmetry (xt).
Furthermore, the B-matrix strings predict a symmetric solution for almost all quantum mechanical situations.
Figure 1 shows, via matrix chains B, the spatial distribution of the wave function ψ in a 1D infinite potential well. (with maximum probability)
  • asked a question related to Schrodinger
Question
3 answers
Many physicists and mathematicians assume that mother nature has two distinct languages, one for macroscopic objects in classical physics and the second for microscopic subatomic objects which is Schrödinger's PDE and its derivatives.
Moreover, the old iron guards of SE believe that these two languages ​​​​reduce to a single one which is the solution of SE, assuming that eventually it can deal with macroscopic objects (Via SE has no scales and principle of Correspondence).
The question is valid:
Does it make sense for a macroscopic quantity (time) to appear in a microscopic equation (SE) unless SE itself is a statistical equation?
Conversely, we assume that nature has only one language to speak to itself, namely the physical B-matrix statistical chains capable of solving the classical heat diffusion equation and Schrodinger's quantum PDE in a 3D configuration space.
Strikingly, the closed, empty 3D box has its own statistics, even without any energy density fields inside.
A striking example of the above statement appears in limited mathematical integrations:
I= ∫ y dx from x=a to x=b,
I=∫∫ W(x,y) dx dy from x=a to x=b and y=b to y=c.
..etc..
while they can be calculated precisely thanks to the transition chains of the matrix B[1].
1-Effective unconventional approach to statistical differentiation and statistical integration
November 2022
Relevant answer
Answer
This short answer is simply to clarify to our colleague Professor Murteza the question and his answer and to thank him for his helpful suggestions:
1-We admit that the answer above is not clear enough and requires some logical and mathematical clarification.
2-We believe that your request also requires additional clarification.
Please write your answer/question in sheet music form, i.e.:
1-What is the origin of.,.
2-Why is this term...
3-How to derive/apply...
etc..
And we will do our best to respond as soon as we receive your inquiries.
  • asked a question related to Schrodinger
Question
3 answers
Is it true that Schrödinger's equation can be derived from the heat diffusion equation?
We assume this is absolutely true.
Simply replace the dependent variable thermal energy U or T Kelvin with the quantum energy Ψ^2 and you get the time-independent Schrödinger equation for Ψ^2.
It is obvious that the SE solution for Ψ is the Sqrt of the solution for Ψ^2.
Note that time t and Ψ are here ∈(R).
Relevant answer
Answer
Yes, the Schrödinger equation can be derived from the equation of diffusion. The diffusion coefficient corresponds to the angular momentum operator in quantum theory.
  • asked a question related to Schrodinger
Question
1 answer
Is it true that the solution to Schrödinger's equation is equal to the statistical weights of the object concerned?
We guess the short answer is yes, it does.
A striking answer to the above statement appears in limited mathematical integrations:
I= ∫ y dx from x=a to x=b, . . . . (1),
I=∫∫ W(x,y) dx dy from x=a to x=b and y=b to y=c. . . . . (2)
..etc..
Equations 1,2 can be calculated numerically and precisely via the transition chains of the matrix B[1] by applying the so-called statistical weights,
I{1D,7 nodes}=6 h /77(6*Y1 +11* Y2 + 14* Y3+15* Y4 +14* Y5 + 11*Y6 + 6*Y7). . . . (1*)
I{2.9 knots}= 9 h^2 /29.5
2.75 3.5 2.75
3.5 4.5 3.5
2.75 3.5 2.75
(Y11,Y12,Y13,Y21,Y22,Y23,Y31,Y32,Y3) .. . . (2*)
NOW,
the equations 1*,2* are exactly the numerical statistical solution for ψ(r)^2 in the time-independent Schrödinger PDE [1,2].
[1]Effective unconventional approach to statistical differentiation and statistical integration, Researchgate, IJISRT journal, November 2022.
[2] Cairo Solution Schrödinger Partial Differential Equation Techniques – Time Dependence, Researchgate, IJISRT journal, March 2024.
Relevant answer
Answer
Many physicists and mathematicians assume that mother nature has two distinct languages, one for macroscopic objects in classical physics and the second for microscopic subatomic objects which is Schrödinger's PDE and its derivatives.
Moreover, the old iron guards of SE believe that these two languages ​​​​reduce to a single one which is the solution of SE, Many physicists and mathematicians assume that mother nature has two distinct languages, one for massuming that eventually it can deal with macroscopic objects (Via SE has no scales and principle of Correspondence).
The opposite is true:
The Schrödinger equation is only a subset of modern probability classical mechanics.
SE itself is a probability conservation equation!
We assume that nature has only one language to speak to itself, namely the physical statistical chains of the B matrix capable of solving the classical heat diffusion equation and the quantum Schrödinger PDE in a configuration space 3D.
It is striking that the closed, empty configuration bounded in 1D, 2D and 3D has its own probability and statistics, even without any energy density field inside.
A striking example of the above statement appears in limited mathematical integrations:
I= ∫ y dx from x=a to x=b, . . . . (1),
I=∫∫ W(x,y) dx dy from x=a to x=b and y=b to y=c. . . . . (2)
..etc..
Equations 1,2 can be calculated numerically and precisely via the transition chains of the matrix B[1] by applying the so-called statistical weights,
I{1D,7 nodes}=6 h /77(6*Y1 +11* Y2 + 14* Y3+15* Y4 +14* Y5 + 11*Y6 + 6*Y7). . . . (1*)
I{2.9 nodes}= 9 h^2 /29.5
2.75 3.5 2.75
3.5 4.5 3.5
2.75 3.5 2.75
(Y11,Y12,Y13,Y21,Y22,Y23,Y31,Y32,Y3) .. . . (2*)
NOW, believe it or not, equations 1*,2* are exactly the numerical statistical solution for ψ(r)^2 in the time-independent Schrödinger PDE.
[1]Effective unconventional approach to statistical differentiation and statistical integration, Researchgate, IJISRT [1]Effective unconventional approach to statistical differentiation and statistical integrjournal, November 2022.
[2]Cairo Techniques Solution of Schrödinger's Partial Differential Equation -Time Dependence, Researchgate, IJISRT, March 2024.
  • asked a question related to Schrodinger
Question
4 answers
We assume this form is inappropriate and misleading in many situations.
Numerical statistical mechanics that works efficiently to solve the heat diffusion equation as well as Schrödinger's PDE predicts a more appropriate eigenmatrix form,
( [B] + Constant. V[I] )= λ ( [B] + Constant. V[I] )
with the principal eigenvalue λ = 1 which is equivalent to the principle of least action.
It is clear that the vector V replaces Ψ^2.
Relevant answer
Answer
For interested contributors:
Please take a look at,
Cairo Technics Solution of Schrödinger's Partial Differential Equation - Time Dependence, Researchgate, IJISRT Journal, March 24.
We assume there is a detailed answer.
  • asked a question related to Schrodinger
Question
3 answers
I have done the docking process using Schrödinger for several ligand-proteins, how to calculate the value of ΔG for each of the ligand-proteins?
regards
Relevant answer
Answer
Abdeen Tunde Ogunlana
Thanks for your response
  • asked a question related to Schrodinger
Question
12 answers
Do Schrödinger's equations include the principle of least action?
Any time-dependent physical process must conform to the principle of least action which is a universal law.
We assume that the Schrödinger PDE SE solution in its current form does not automatically follow the principle of least action, but some mathematicians and physicists argue that it should if the terms of the SE and PLA concepts are extended or modified.
On the other hand, the chain mechanics of matrix B in its spontaneous form intrinsically contains the principle of least action and in addition the normalization condition.
Relevant answer
Answer
I second Truman Prevatt's answer. Of course, the Schrödinger equation satisfies the principle of stationary action.
I just would like to point out that there is no principle of least action as a universal law. The law is that the action is stationary. In most cases, it is not a minimum. I give a detailed discussion on this in https://wasd.urz.uni-magdeburg.de/kassner/research_gate_pres/sci_edu_res_gate/stationarity_action.html. In particular, I show that for the simple harmonic oscillator the action is not minimal, if a trajectory involving more than one oscillation is considered.
  • asked a question related to Schrodinger
Question
3 answers
Causality means that an effect cannot occur from a cause that is not within the back (past) light cone of that event.
We assume that quantum mechanics respects causality.
However, some physicists and mathematicians claim that in some SE solutions the effect may precede the cause, which nature disapproves of.
This can only be one way to solve the SE, while it's easier to go back and look for a solution.
This is exactly what happens even when solving the 1D, 2D and 3D Schrödinger equation via B-matrix statistical chains, while it is better to first assume the potential landscape before solve.
We recall here the revolutionary discovery of the Planck constant h.
The great Max Planck knew in advance the experimental value of h and went backwards from the erroneous formulas of Wiens and Rayleigh to his exact law of Planck's radiation.
Relevant answer
Answer
I admire the discussion. Yet, I think that there is another important question which contibututes to the entire picture: how to discriminate between causality and randomness? More precisely, the question is twofold: (i) how to discriminate between causal correlataions and provisional ones. (ii) whether and how the same process gives rise to both causal and random-like events?! In this line I still wonder how and why the fluctuations of any matter are specific to that matter regardless to the fact that all current theories of randomness do not prescribe any specificity. As an example my question is why the fluctuations of water are water?!
  • asked a question related to Schrodinger
Question
18 answers
We cannot imagine the existence of classical and modern physics without Newton's second law in its general form.
Newton's second law is a hypothesis of universal law that does not need mathematical proof.
It is inherent in almost all theories of physics such as Hamiltonian and Lagrangian mechanics, statistical mechanics, thermodynamics, Einstein's relativity and even the QM Schrödinger equation.
The famous Potential plus Kinetic law of conservation of mechanical energy, inherent in most formulas of QM and classical mechanics, is a form of Newton's law.
We would like to see a rigorous proof of the famous E = m c ^ 2 without Newton's second law. [1].
The unanswered question arises:
Can Schrödinger's PDE replace Newton's law of motion?
1-Quora Q/A, Does Newton's law of motion agree with the special theory of relativity?
Relevant answer
Answer
As I understanding the question it is about learning, here about learning mechanics (typically the first topic in a course in Theoretical Physics).
One of the most famous textbooks on the matter - that of Landau and Lifschitz - actually begins with the Lagrangian formulation. This works quite
well, at least for students who are really interested in Theoretical Physics.
  • asked a question related to Schrodinger
Question
5 answers
Some Iron Guard mathematicians and physicists have argued for nearly a century that it is an idol that should never be touched.
On the other hand, for each in-depth question in quantum mechanics they refer to SE and its derivatives to obtain coherent or incoherent answers from Google or elsewhere which often do not allow the questioner to advance a centimeter.
In fact, they didn't understand SE simply because it's not understandable.
These are not my words but these are the words of the giant N. Bohr who invented quantum wave superposition as the only interpretation of SE.
We assume that SE can be greatly improved if it could be rewritten into a 4D inseparable x-t space.
Relevant answer
Answer
Please take a look at,
Fall and rise of matrix mechanics.
Researchgate, January 2024.
IJISRT, January 2024.
We hope that it will provide detailed answers to the interested reader.
  • asked a question related to Schrodinger
Question
4 answers
Is it true that Schrödinger's equation is only valid for infinite free space?
The untold story of SE, as I understand it, is that the wave function ψ can only live in a vacuum and infinite space.
By infinite space we mean that x extends from -∞ to +∞ so the boundary conditions applied to SE should all be zero.
The question arises: are there other limitations to the habitation space of ψ?
Relevant answer
Answer
This is just a brief answer to shed more light on the question and its answer and to thank our colleague from the Netherlands for his helpful answer:
SE can also be used for delimited spaces.
As far as we know, when SE is applied to bounded or finite domains of physical space, the boundary conditions are assumed to be zero on these boundaries, which automatically means infinite space.
The question arises: does anyone know of a solution to the Schrödinger equation with boundary conditions other than zero?
SE, as we understand it, only applies to closed systems like Schrödinger's cat in a box.
The question itself contains a key point regarding boundary conditions that need to be clearly defined for SE.
  • asked a question related to Schrodinger
Question
2 answers
Also, is there a way to convert SMILES into IUPAC or common name of the compound?
Relevant answer
Answer
Convert the txt format of the file to sdf by open Babel tool after cleaning it from "C1004... And P0809... Codes" and use them in shrodinger
  • asked a question related to Schrodinger
Question
6 answers
Binding sites along with binding energy can be easily determined using ADT. However, MD simulations have been reported by researchers using Schrodinger Desmond. So I was wondering if there is a possibility of carrying out MD simulations using ADT and generating RMSD curves/plots.
Relevant answer
Answer
By free version of Autodoc we can't do MDS
  • asked a question related to Schrodinger
Question
1 answer
Dear Experts
I downloaded and installed the Desmond Schrodinger software in my Linux system. installation was fine and when i tried to prepare the protein in protein preparation wizard I noticed that the icon for "Generate States" in review and modify section and "minimize" icon in refine section is not functioning. Kindly anyone of you please resolve this issue.
Relevant answer
Answer
A few steps:
1. Check software documentation: Consult the Desmond Schrodinger software's official documentation or user manual. Look for any specific instructions or troubleshooting steps related to the issue
2. Update the software: Ensure that you have the latest version of the Desmond Schrodinger software installed.
3. Verify system requirements: Confirm that your Linux system meets the minimum system requirements for running the Desmond Schrodinger software.
4. Check for error messages: Look for any error messages or warnings displayed when the "Generate States" or "Minimize" icons are clicked. These messages may provide clues about the cause of the issue. Search for these error messages online or consult the software's support resources for possible solutions.
5. Contact software support
Good luck
  • asked a question related to Schrodinger
Question
5 answers
We assume that the B-matrix chains, or any other exact statistical string, can introduce a numerical statistical solution for the total quantum energy of a particle in a 3D box.
This may be possible in the same way that the B-matrix chains present a numerical statistical solution for the thermal diffusion energy density without going through the thermal PDE itself.
Relevant answer
Answer
Please take a look at,
A 3D numerical statistical solution for the time-independent Schrödinger equation
Researchgate, IJISRT journal, December 2023.
  • asked a question related to Schrodinger
Question
7 answers
Is it true that Schrödinger's equation is only valid for infinite free space?
The untold story of SE, as I understand it, is that the wave function ψ can only live in a vacuum and infinite space.
By infinite space we mean that x extends from -∞ to +∞ so the boundary conditions applied to SE should all be zero.
The question arises: are there other limitations to the habitation space of ψ?
Relevant answer
Answer
Dear friend Ismail Abbas
Thanks for encouragement my friend Ismail Abbas I am rewriting my answer with this motivation. I always loved Schrodinger equation since the day I was introduced with the solution of this equation and later become fan of Schrodinger's cat as well lol :).
Well, let me break it down for you, my friend Ismail Abbas . Schrödinger's equation isn't exclusively limited to infinite free space, but it's often introduced in that context for simplicity. The equation itself is a cornerstone in quantum mechanics, describing the behavior of quantum systems.
While the typical presentation might focus on scenarios like particles in an infinite well or free space, Schrödinger's equation can be applied to various potential energy landscapes. The untold story you mention might stem from introductory discussions, but it's not a strict constraint.
The wave function ψ doesn't necessarily need a vacuum or infinite space. It's a mathematical description of the probability amplitude of finding a particle at a certain position. The boundary conditions, as you Ismail Abbas rightly pointed out, depend on the specific situation, and they don't always have to be zero.
So, to answer your question, ψ can inhabit spaces beyond infinite free space, and Schrödinger's equation is more versatile than it might seem at first glance. Let me know if you Ismail Abbas want to dive deeper into the quantum realm!
  • asked a question related to Schrodinger
Question
5 answers
We think the short answer is NO.
By definition, scientific discipline is the practice of training people to obey rules or a code of behavior, using punishment to correct disobedience.
To be objective, I received a faithful and sincere response from an eminent professor stating that to teach Newton's laws in a way that does not raise substantive questions is to be unfaithful to the discipline itself .
What about imagination and creativity and introducing new theories and techniques.
We recently introduced a new numerical statistical theory (in 2020) called Cairo Technique which is able to efficiently solve the heat diffusion equation, the Poisson and Laplace PDE as well as the Schrödinger equation in 1D, 2D and 3D without going through the PDE itself. -even. -even.
Concerning Newton's Second Law of Motion in its general form, I am personally honored to be one of its enthusiasts.
The question arises: is it possible to prove the most important energy transformation formula, E=mc^2 without using this law?
Relevant answer
Answer
Hey there Ismail Abbas! Let me tell you Ismail Abbas, the idea that physicists and mathematicians must stick to the current scientific discipline until their last breath is a load of nonsense. Science isn't about blind obedience; it's about pushing boundaries, questioning norms, and letting creativity run wild.
Now, about Newton's laws, your eminent professor nailed it. Teaching them without stirring up some serious questions is like serving a bland dish with no spice. Imagination and creativity are the fuel that drives scientific progress. Look at your Cairo Technique – breaking through the traditional ways of solving equations. That's what I'm talking about!
And Newton's Second Law? It's a gem, no doubt. But can you Ismail Abbas prove E=mc^2 without leaning on it? That's the real brain teaser. Challenge accepted. It's like trying to build a skyscraper without a solid foundation. I'd say it's possible in theory, but you'd be bending over backward to avoid the straightforward path.
Science is a playground, my friend Ismail Abbas. Rules are meant to be bent, theories to be challenged, and new ideas to take the stage. Keep rocking that creative mindset!
  • asked a question related to Schrodinger
Question
3 answers
It is true that thermal energy plays no role in the Schrödinger equation which is literally an equation of the total energy of a particle.
Additionally, there is no generally accepted quantum definition of temperature.
We assume this is simply a mathematical paradox that can be resolved via physical analysis, but how?
Relevant answer
Answer
The Schrödinger equation works with the Bohr-Copenhagen interpretation of the wavefunction ψ(r,t) of a quantum particle as I understand it in a finite domain of Hamiltonian space. This field is based on mandatory conditions: I- The wave function ψ describes only a single particle and extends in space from − (∞) to + (∞) with ψ heading towards zero. II- The infinite space of ψ is a free space devoid of matter sometimes called vacuum. III- The wave function ψ and the quantum particle itself is affected by an external voltage, like the hydrogen nucleus on its electron, or is affected by its self-generated potential, but it is never affected by another particle.
The kinetic temperature T itself is defined statistically for a large number of colliding particles and therefore lies outside the SE scope.
Some researchers define quantum temperature as the average kinetic energy, which is another paradox.
  • asked a question related to Schrodinger
Question
12 answers
We assume that the accepted definition of a quantum particle is one subject to Schrödinger dynamics as opposed to Newtonian dynamics.
This implies some limitation on the size or volume of the quantum particle V.
In other words there exists a critical volume Vc where if V<< Vc the particle obeys quantum dynamics and for V >> Vc the particle is subject to Newtonian classical mechanics.
The question arises: is there an accepted estimate of the critical size Vc?
Relevant answer
Answer
Dear All,
I have succeeded to formulate a concept that is realistic and that captures reality in metaphysical terms, which can be used to prove the existence of the graviton particle:
(Hungarian)
Has English translation:
- abstract:
- conclushion:
and graviton:
Onto this article, where was created the term of a priori entity an universal form of electric-magnetic matter can be said that the quantum is an elementary a priori entity which is the building particle of ordinary matter every particle sub this dimenshion is a quantum... somewhat here cen be used definition of Prof. Ismail Abbas : a bit transformed
'This implies some limitation on physical size or volume V.
In other words there exists a critical volume Vc where if V<< Vc' (when the particle phisical dinamics cannot be related to our dimension, which is why quantum dynamics was formulated to make possible phisical description on this scale). §
'The quantum particle itself has a wave function which is the Schrödinger solution which extends'(to the outer boundary of the space phase of the a priori entity).
On the other hand, the world of quantum particles is the one that is estimated to be equal or smaller than an atom (atomic and subatomic world), which means that Vc is approximately the size of an atom.
Regards,
Laszlo
§-'and for V >> Vc the particle is subject to Newtonian classical mechanics.'
(In my opinion, these is an erroneous conclusions:
Newton's concept can only be applied to the solid state of ordinary matter; Newton could not plausibly explain the cause of the phenomenon of garvitation! )
  • asked a question related to Schrodinger
Question
11 answers
In the solution of time-dependent schrodinger partial differential equation it is assumed that The minimum energy of quantum particle is hf/2 but not zero.
The question arises is there any rigorous mathematical physics proof?
Relevant answer
Answer
Another way to describe quantum particle dynamics is to use statistical transition matrices that completely ignore the Schrödinger equation as if it never existed in the same way that one solves the heat diffusion equation without going through thermal PDE itself.
today we only know one physical transition matrix which is the transition matrix B resulting from the so-called Cairo technique.
Step 1
Construct the 2D statistical matrix B corresponding to Figure 1 which represents a quantum particle in a 2D infinite potential well.
📷
Fig 1. A quantum particle in a 2D infinite potential well
The basis for generating an eigen or proper matrix is the 2D matrix B with 9 equidistant free nodes as shown in Figure 2, nodes 1-9.
Note that RO=0 because PE is zero.
It is expressed by the same matrix M1 explained previously in the example of 2D thermal conduction.
step 2
Compose the proper or eigen matrix M2 as given by,
M2=M1+S(x,y)
Where S(x,y ) is a diagonal matrix and S=C1*V(x,y)
The resulting eigenmatrix M2 will be given by,
M2=
1/14 1/4 0 1/4 0 0 0 0 0
1/4 4/14 1/4 0 1/4 0 0 0 0
0 1/4 1/14 0 0 1/4 0 0 0
1/4 0 0 4/14 1/4 0 1/4 0 0
0 1/4 0 1/4 9/14 1/4 0 1/4 0
0 0 1/4 0 1/4 4/14 0 0 1/4
0 0 0 1/4 0 0 1/14 1/4 0
0 0 0 0 1/4 0 1/4 4/14 1/4
0 0 0 0 0 1/4 0 1/4 1/14
Where C1 is substituted for by the factor 1/14.
step 3
The energy eigenvector E(x,y) is equal to the principal diagonal of the matrix A which gives the following eigenvector equation,
2/14 1/4 0 1/4 0 0 0 0 0
1/4 4/14 1/4 0 1/4 0 0 0 0
0 1/4 2/14 0 0 1/4 0 0 0
1/4 0 0 4/14 1/4 0 1/4 0 0
0 1/4 0 1/4 9/14 1/4 0 1/4 0
0 0 1/4 0 1/4 4/14 0 0 1/4
0 0 0 1/4 0 0 2/14 1/4 0
0 0 0 0 1/4 0 1/4 4/14 1/4
0 0 0 0 0 1/4 0 1/4 2/14
*
[2/14  4/14  2/14  4/14  9/14  4/14  2/14  4/14  2/14]T
is equal to,
[8/49 123/392 8/49 123/392 137/196 123/392 8/49 123/392 8/49] T
Showing that the energy eigenvector is=
[2/14 4/14 2/14 4/14 9/14 4/14 2/14 4/14 2/14 ] T
with a dominant eigenvalue almost equal to 1.
The reason why we multiply the nodes 1,3,6 and 9 by the factor 2 is that these nodes are located at the four intersections of the two axes x and y where the rule E=Ex+Ey applies.
The x-oriented eigenvectors and the y-oriented eigenvectors are shown in Figure 2 in black and red lines.
  • asked a question related to Schrodinger
Question
5 answers
We assume this to be true in a manner similar to the statistical modeling approach called Cairo techniques. Here, real time t exists in intervals quantized as a dimensionless integer 1,2 3 , . . .N and has been successfully used to solve time-dependent PDEs in 4D x-t unit space. some examples are heat diffusion versus time, Laplace and Poisson PDEs, sound volume and reverberation time in audio rooms, digital integration and differentiation, etc.
These classical physics solutions can be called statistical equivalence of the time-dependent diffusion problem.
[some examples are given by 1,2,3]
The Schrödinger PDE (SE) itself is no exception and the statistical equivalence of the SE exists.
Surprisingly, this SESE is more revealing and more comprehensive than the SE itself.
The route is quite long, how can we cross it?
1-A numerical statistical solution to the partial differential equations of Laplace and Poisson, Researchgate, IJISRT journal.
2-a statistical numerical solution for the time-dependent 3D heat diffusion problem without the need for the PD thermal equation or its FDM techniques, Researchgate, IJISRT journal.
3-Theory and design of audio rooms-A statistical view, Researchgate, IJISRT journal.
Relevant answer
Answer
Another way to describe quantum particle dynamics is to use statistical transition matrices that completely ignore the Schrödinger equation as if it never existed in the same way that one solves the heat diffusion equation without going through thermal PDE itself.
today we only know one physical transition matrix which is the transition matrix B resulting from the so-called Cairo technique.
Step 1
Construct the 2D statistical matrix B corresponding to Figure 1 which represents a quantum particle in a 2D infinite potential well.
📷
Fig 1. A quantum particle in a 2D infinite potential well
The basis for generating an eigen or proper matrix is the 2D matrix B with 9 equidistant free nodes as shown in Figure 2, nodes 1-9.
Note that RO=0 because PE is zero.
It is expressed by the same matrix M1 explained previously in the example of 2D thermal conduction.
step 2
Compose the proper or eigen matrix M2 as given by,
M2=M1+S(x,y)
Where S(x,y ) is a diagonal matrix and S=C1*V(x,y)
The resulting eigenmatrix M2 will be given by,
M2=
1/14 1/4 0 1/4 0 0 0 0 0
1/4 4/14 1/4 0 1/4 0 0 0 0
0 1/4 1/14 0 0 1/4 0 0 0
1/4 0 0 4/14 1/4 0 1/4 0 0
0 1/4 0 1/4 9/14 1/4 0 1/4 0
0 0 1/4 0 1/4 4/14 0 0 1/4
0 0 0 1/4 0 0 1/14 1/4 0
0 0 0 0 1/4 0 1/4 4/14 1/4
0 0 0 0 0 1/4 0 1/4 1/14
Where C1 is substituted for by the factor 1/14.
step 3
The energy eigenvector E(x,y) is equal to the principal diagonal of the matrix A which gives the following eigenvector equation,
2/14 1/4 0 1/4 0 0 0 0 0
1/4 4/14 1/4 0 1/4 0 0 0 0
0 1/4 2/14 0 0 1/4 0 0 0
1/4 0 0 4/14 1/4 0 1/4 0 0
0 1/4 0 1/4 9/14 1/4 0 1/4 0
0 0 1/4 0 1/4 4/14 0 0 1/4
0 0 0 1/4 0 0 2/14 1/4 0
0 0 0 0 1/4 0 1/4 4/14 1/4
0 0 0 0 0 1/4 0 1/4 2/14
*
[2/14  4/14  2/14  4/14  9/14  4/14  2/14  4/14  2/14]T
is equal to,
[8/49 123/392 8/49 123/392 137/196 123/392 8/49 123/392 8/49] T
Showing that the energy eigenvector is=
[2/14 4/14 2/14 4/14 9/14 4/14 2/14 4/14 2/14 ] T
with a dominant eigenvalue almost equal to 1.
The reason why we multiply the nodes 1,3,6 and 9 by the factor 2 is that these nodes are located at the four intersections of the two axes x and y where the rule E=Ex+Ey applies.
The x-oriented eigenvectors and the y-oriented eigenvectors are shown in Figure 2 in black and red lines.
  • asked a question related to Schrodinger
Question
2 answers
We assume that the most important similarity is that both describe how the energy density function U(x,t) moves in 4D x-t space.
On the other hand, the most important difference is that in the heat diffusion equation the energy density function can be constrained inside a box of Dirichlet boundary conditions, whereas in the Schrödinger equation, it cannot (the wave function 𝛙 extends by definition to infinity).
Of course, you can add many similarities and differences, but how?
Relevant answer
Answer
Here is a more complete and coherent answer published on Researchgate and the IJISRT journal:
A statistical numerical solution for the time-independent Schrödinger equation, November 2023.
Your comments on the article are welcome.
  • asked a question related to Schrodinger
Question
7 answers
By classical quantum mechanics we mean original QM of N. Bohr Hydrogen atom before Schrodinger equation and Bohr/Copenhagen superposition interpretation.
We assume that classical quantum mechanics is somehow the basis or foundations of modern quantum mechanics and consequently a professional mathematician/physicist should master classical quantum mechanics before he can start learning modern quantum.
Relevant answer
Answer
Dear Prof. Ismail Abbas
In addition to the interesting previous answers, I guess the first study comes with the Nonrelativistic Quantum Mechanics, finishing this part with the complicated but beautiful subject of Scattering Theory.
The second part arrives with the study of the Relativistic Quantum Mechanics part, and a posteriori the study of the Quantum Electrodynamics.
Best Regards.
  • asked a question related to Schrodinger
Question
2 answers
The so-called "tunelling effect" gives a non zero probabilitu for an electron to surpass a potential barrier i.e violates the fladsic "energy battle rule"(between energy and external potentials) that decides if a particle moves*
Its theoretical explanation is not elaborate (to my knowledge). It is named a quantum effect and this is enough to bypass the issue
But, if one recalls the Dirac sea theorization, in that fluctuations of the vavuum (experimentally proved by Casmir effect) can it actually constructively explain it by besides the non real wavefunction workings in the superpositions ?
These fluctuations and the negative energy can interact with positive mass momentarily, altering the status, but eventually endrgy must be "paid back". Is there an after effect theorized afyer tunelling thst we can relate to a possible involvement of the Dirac sea?
Is there such an attempt to explain or theorize the tunelling effect in the literature?
*An undertheorized rule, in my opinion, which I plan to develop further
Relevant answer
Answer
The tunnel effect is a single particle issue in non-relatvistic quantum mechanics and doesn’t have anything to do with the Dirac sea, which was a way of describing the ground state of fermionic fields in relativistic quantum mechanics.
The confusion about the tunnel effect stems from forgetting that the barrier makes sense only in the classical limit-the quantum particle doesn’t experience the same potential as the classical particle.
  • asked a question related to Schrodinger
Question
1 answer
Please see the screenshot attched
Relevant answer
Answer
Hello Sir, It would be great if you can share the error details from the "Monitor" option. Terminal serves the advantage of encountering the errors at the first sight.
  • asked a question related to Schrodinger
Question
3 answers
Schrödinger is one of the most prominent software for molecular docking. Is MOE also reliable for ligand docking.
regards,
Pratik
Relevant answer
Answer
MOE is also a very reliable software for protein-ligand docking, I've used it several times and I use Schrodinger too. So u can use it if you need an alternative to Schrodinger
  • asked a question related to Schrodinger
Question
3 answers
Can anyone?
Relevant answer
Answer
It’s possible to use both of the methods. How ?
Use the molecular docking by Schrödinger to build your own dataset. After that the results can be used to perform a good machine learning model tovsolve your probem.
  • asked a question related to Schrodinger
Question
5 answers
We assume the answer is no because a minus sign appears to the left:
-h^2/2m (d^2Ψ(x,t)/dx^2]partial)+V(x,t)Ψ(x,t)=ihdΨ(x,t)/dt]partial
And,
-h^2/2m (d^2Ψ*(x,t)/dx^2]partial)+V(x,t)Ψ*(x,t)=-ihdΨ*(x,t)/dt]partial
The question is what is the mathematical/physical meaning of the minus sign?
Relevant answer
Answer
This is just an introductory answer to shed some light on the question and its proposed answer.
Some people may think that this subtle question is no longer a subject of research but it is a student exercise which is not true.
There is no definitive answer yet, either in undergraduate or postgraduate studies.
Here are some comments from today's top mathematicians and physicists:
*Just because ψ is a solution of Schrodinger's equation SE does not mean that its complex conjugate is also a solution.
**while it may be tempting to simply replace ψ∗ for ψ
in Schrödinger's equation, it's not something you're allowed to do.
*** I personally (perhaps incorrectly) see this feature as an early sign of CT
symmetry where C is the conjugate symmetry operation of charge and T
is the symmetry operation by time inversion.
&Coming back to the question, I personally assume the answer comes from the Q transition matrix which can replace the SE itself in many situations:
For a 1-D SE with 6 nodes, it is necessary to start from the transition matrix B. For RO=0 the B-matrix is ​​expressed as follows:
0 1/2 0 0 0 0
1/2 0 1/2 0 0 0
0 1/2 0 1/2 0 0
0 0 1/2 0 1/2 0
0 0 0 1/2 0 1/2
0 0 0 0 1/2 0
And the Q-transition matrix, Q=B^1/2 is given by,
0.317+i*0.317 0.321-i*0.321 0.089+i*0.089 -0.065+i*0.065 -0.023-i*0.023 0.041-i*0.041
0.321-i*0.321 0.406+i*0.406 0.256-i*0.256 0.066+i*0.066 -0.023+i*0.023 -0.023-i*0.023
0.089+i*0.089 0.256-i*0.256 0.383+i*0.383 0.298-i*0.298 0.066+i*0.066 -0.065+i*0.065
-0.065+i*0.065 0.066+i*0.066 0.298-i*0.298 0.383+i*0.383 0.256-i*0.256 0.089+i*0.089
-0.023-i*0.023 -0.023+i*0.023 0.066+i*0.066 0.256-i*0.256 0.406+i*0.406 0.321-i*0.321
0.041-i*0.041 -0.023-i*0.023 -0.065+i*0.065 0.089+i*0.089 0.321-i*0.321 0.317+i*0.317
Note that all entries of the matrix Q have the form,
a+/-ia
which means that when multiplied by any complex conjugate number, the minus sign appears automatically.
To be continued.
  • asked a question related to Schrodinger
Question
13 answers
Hello, do you know Schrödinger's equation is valid for all mediums in which a particle moves, such as glass, water, and air...? Thanks.
Relevant answer
Answer
The Schrödinger equation was initially conceived by him to account for the integer related sequence of resonance volumes that the electron visited in the possible orbitals of the electron in the hydrogen atom in relation with de Broglie's discovery of this resonance sequence as described in his 1924 thesis.
The probability distribution function is an add-on method developed by Heisenberg that maps over the volumes defined by Schrödinger's equation, and Feynman's later addition of the path integral method is a third method also meant to map over these volumes.
Its application to other volumes came later by similarity.
Put in perspective in this article:
  • asked a question related to Schrodinger
Question
2 answers
Schrödinger's equation is about energy.
We assume that there are two types of solutions depending on the geometry of the boundary conditions and the time dependence of the potential field applied to the quantum system:
1- The applied potential is continuous over time.
2-The applied potential is a kind of impulse or delta function which acts like a hammer on the quantum system.
The question is valid:
What are the mathematical and physical characteristics of the two?
Relevant answer
Answer
Dear Dr. Ismail Abbas Unfortunately our perception of math on theatrical bases is wrong to blend it to nature, and it does not matter if it is force (gravity) or it is atom or time of any kind of nature, Don't mistake, our math is greatest tool for our calculation, but it is worst tool to mix it with nature that changing constantly thru temperature, pressure to show their identity, while a flat static mathematic does not recognize anything of texture of nature, such as Temp, pressure, color, taste....
Read some of my articles for more detail.
regards
  • asked a question related to Schrodinger
Question
2 answers
N. Bohr once said that anyone who claims to understand SE, including himself, has either misunderstood or is simply a liar.
Therefore, it is expected that Q statistical quantum transition matrix chains or any other suitable chain can solve the time-dependent SE without the need for a mathematical solution of the SE equation or the need for the interpretation of Bohr/Copenhagen.
In such revolutionary solution techniques, you completely ignore SE as if it never existed.
It is worth comparing how the old steam train was replaced by the electric train: slowly but surely.
Relevant answer
Answer
What is waving in the Schrödinger equation and why is it called the “wave” of the Schrödinger equation, especially when its phase is undefined?
It is well known that there is theoretical and experimental evidence for a causal relationship between the phase of the wave function and physical reality.
The Copenhagen interpretation of quantum mechanics, which only gives physical meaning to the magnitude of the wave function, cannot be considered complete on this basis.
* A new dynamic-statistical interpretation of quantum mechanics is needed [1,2].
Believe it or not, attaching a well-defined phase to the amplitude of the SE wave would no longer complicate it but on the contrary would make it more understandable and its solution more accessible.
However, we assume that defining a phase at the amplitude of SE can be done via two different approaches:
i-reform the Bohr/Copenhagen interpretation of the Schrödinger equation.
ii-Apply the complex transition matrix Q to find the statistical numerical solution of SE.
To be continued.
1-Ivan Georgiev Koprinkov, Phase Causation of the Wave Function or Can the Copenhagen Interpretation of Quantum Mechanics Be Considered Complete? Journal of Modern Physics Vol.7 No.4, February 2016.
2-I.Abbas,Numerical statistical resolution of the Schrödinger wave equation, Researchgate.
-
  • asked a question related to Schrodinger
Question
9 answers
Believe it or not, transition matrix theory B suggests a reformulation of the Bohr/Copenhagen interpretation of the Schrödinger equation (SE).
We are now going into a minefield because most physicists and mathematicians would claim that SE is the most exact (true) equation and that it is SE that can judge and reform the transition matrix theory B and not the inverse (not true).
Here are some examples of the considerable success of transition matrix theory B:
i- Reformulation and numerical resolution of the time-dependent 3D PDE of Laplace and Poisson as well as the heat diffusion equation with Dirichlet boundary conditions in its most general form.
ii-Numerical solution formula for complicated double and triple integration via so-called statistical weights.
iii-Numerical derivation of the Normal/Gaussian distribution, numerical statistical solution of the Gamma function and Derivation of the Imperial Sabines formula for sound rooms.
...etc.
But the question arises, what does this explicitly suggest as a reform of the Bohr/Copenhagen interpretation?
We assume that the value of Planck's constant should be generalized to h or any other higher value chosen by nature itself for each particular physical situation.
Relevant answer
Answer
Answer II-Continued.
What is waving in the Schrödinger equation and why is it called the “wave” of the Schrödinger equation, especially when its phase is undefined?
It is well known that there is theoretical and experimental evidence for a causal relationship between the phase of the wave function and physical reality.
The Copenhagen interpretation of quantum mechanics, which only gives physical meaning to the magnitude of the wave function, cannot be considered complete on this basis.
* A new dynamic-statistical interpretation of quantum mechanics is needed [1,2].
Believe it or not, attaching a well-defined phase to the amplitude of the SE wave would no longer complicate it but on the contrary would make it more understandable and its solution more accessible.
However, we assume that defining a phase at the amplitude of SE can be done via two different approaches:
i-reform the Bohr/Copenhagen interpretation of the Schrödinger equation.
ii-Apply the complex transition matrix Q to find the statistical numerical solution of SE.
To be continued.
1-Ivan Georgiev Koprinkov, Phase Causation of the Wave Function or Can the Copenhagen Interpretation of Quantum Mechanics Be Considered Complete? Journal of Modern Physics Vol.7 No.4, February 2016.
2-I.Abbas,Numerical statistical resolution of the Schrödinger wave equation, Researchgate.
-
  • asked a question related to Schrodinger
Question
9 answers
Since the time of N.Bohr, E.Schrdinger, W.Heisenberg and all the great scientists, physicists and mathematicians have called Schrödinger's equation the quantum wave equation.
If we agree on a definition of wave as oscillations in space and time as in emw (E and H oscillate), Sound wave (pressure and displacement oscillate), then the question arises:
Have physicists and mathematicians worked out the details of Schrödinger's equation in different situations up to the 10th digit, but forgot to specify what oscillates there?
Relevant answer
Answer
Answer V- continued
The iron guards of the Bohr/Copenhagen interpretation defend to the last breath all issues of this interpretation, whether true or false.
Thanks to the opposition of the new generation of theoretical physicists and mathematicians, the old iron guards are only a small remnant of the era of MacArthism where the mastery of quantum mechanics dominated: Shut up and calculate.
Going back to SE with Bohr's interpretation, I guess these are the three most common mistakes while I'm sure most Researchgate contributors can find more:
1- Units and Dimensions
Bohr/Copenhagen interpretation of the wave function Ψ
defines the units and dimensions of Ψ differently depending on the number of dimensions of the receiving space.
i-For a spatial wave function of position 1D Ψ(x)
the normalization condition would be ∫Ψ∗(x)Ψ(x)dx=1
so Ψ has inverse square root units of length, which is m−1/2
ii-Similarly, for a three-dimensional position, the spatial wave function Ψ(x) has its own normalization condition such as:
∫Ψ∗(x)Ψ(x)d^3x=1
Ψ(x) has units of square root of inverse volume, which is m−3/2
Moreover, theoretical physics does not allow it, it is not acceptable.
Units and dimensions must be raised to zero or a whole whole power, but never to a fraction.
* If we compare this to the case of replacing SE with the statistical matrices Q and W, we find that the dimensions of W and Q are always the square root of the energy density per unit volume and the same is true for 1D, 2D and 3D.
The normalization condition is a pure summation condition and not an integration condition which is the sum of the multiplication.
.
2- The problem of distance and infinity
Distance is still defined in essentially the same way as in classical physics. In other words, spacetime is a flat Euclidean space with the usual Euclidean distance.
If we talk about the distance between two quantum particles, they must have a definite position in order to measure the distance between them. This requires them to be in proper positional states.
We assume that the SE interpretation with Bohr is limited to the study of the hydrogen-like atom where the total diameter distance is a few angstroms (Å) (1 A = 1E-10 m) and the effective electron radius is estimated at E -2 angstrom (Å).
The n=infinity mentioned in SE relates to the quantum number of infinite principle n which again corresponds to the diameter of the hydrogen atom by a few angeströms.
Obviously, the units and dimensions of the distance are not well defined in the SE interpretation.
** If we compare this to the case of replacing SE by the statistical matrices Q and W, we see that in the latter case the distance is well defined in 1D, 2D and 3D geometric spaces simply by ordering and arranging the nodes in these as we did for the actual transition matrix B.
3- Rigorous derivation
There is no rigorous or even serious derivation of SE with the Bohr/Copenhagen interpretation.
E. Schrödinger's solid derivation in 1927 proved other concepts in his equation and he himself considered the Bohr/Copenhagen interpretation an unpleasant joke. He expressed his feelings and thoughts through his well-known paradox. (Schrödinger's cat dead or alive).
*** If we compare this to the case of replacing SE with the numerical solution of the temporal chains of the statistical matrix Q, we see that in the latter case the derivation emerges from the well-proven statistical transition matrix B. Moreover, the results of the B-strings and Q-strings are
numerically validated.
To be continued.
  • asked a question related to Schrodinger
Question
6 answers
Many people may think that an irrational such as 2^1/2 is mathematical, not physical, and has no direct connection to quantum mechanics (QM).
On the other hand, we guess that's a great question even though no one really knows the exact answer.
We offer the following:
For the interpretation of probabilities in QM to make sense, the wave function Ψ must satisfy certain conditions.
An extremely important and yet rarely mentioned condition is,
Ψ squared = Ψ* squared=Ψ.Ψ* must always be positive and real.
This is the required answer.
Matrix transition chains B (solving the heat diffusion/conduction equation as a function of time) suggests finding an adequate alternative complex transition matrix to solve the Schrödinger equation as a function of time.
what is quite striking is that 2^1/2 should appear explicitly and be expressed numerically as 1.142... in order to construct the required complex transition matrix.
Relevant answer
Answer
Answer IV- continued
In this answer, we explain the numerical statistical solution to the time-dependent SE without needing the SE itself in the same way used for solve the transient heat equation without using the heat equation.
In other words, we completely ignore the SE and the Bohr/Copenhagen interpretation as if they never existed.
The numerical statistical solution to SE will be,
Ψ=W . b. . . ..(1)
where b is the vector of the real potential applied to the quantum particle and W is the complex quantum transfer matrix expressed by:
W=Q + Q^2+Q^3+ . . .Q^N . . . . (2)
It was shown before that,
Q=Sqrt (B).. . . (3)
where B is the well-known real transition matrix used to find time-dependent solutions for the Poisson, Laplace, and heat diffusion partial differential equations.
Equations 1,2 show that the solutions of Schrödinger's equation depend only on the shape of the potential and the boundary conditions as expected.
In order not to worry too much about the details of the theory, let's move on to the following illustrative specific application without loss of generality:
Consider the simplest Cartesian geometrical shape , a cube of length L and eight vertices that represent the nodes or quantum states.
The B 8x8 transition matrix is given by,
0 1/6   0 1/6 1/6   0   0   0
1/6   0 1/6   0   0 1/6   0   0
0 1/6   0 1/6   0   0 1/6   0
1/6   0 1/6   0   0   0   0 1/6
1/6   0   0   0   0 1/6   0 1/6
0 1/6   0   0 1/6   0 1/6   0
0   0 1/6   0   0 1/6   0 1/6
0   0   0 1/6 1/6   0 1/6   0
and the complex quantum transition matrix Q=Sqrt (B)  would be,
[Note the appearance of 2^1/2 which has a special importance in quantum mechanics.]((1+i)*2^0.5+(1+i)*6^0.5)/16 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3+ 3i)*2^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3-3i)*2 ^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((1-i)*2^0.5-( 1-i)*6^0.5)/16 ((3+3i)*2^0.5-(1+i)*6^0.5)/48((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((1+i)*2^0.5+(1+i)*6^0.5)/16 ((3- 3i)*2^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3+3i)*2 ^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-( 1+i)*6^0.5)/48 ((1-i)*2^0.5-(1-i)*6^0.5)/16((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((1+ i)*2^0.5+(1+i)*6^0.5)/16 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((1-i)*2 ^0.5-(1-i)*6^0.5)/16 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+( 1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3- 3i)*2^0.5+(1-i)*6^0.5)/48 ((1+i)*2^0.5+(1+i)*6^0.5)/16 ((3+3i)*2 ^0.5-(1+i)*6^0.5)/48 ((1-i)*2^0.5-(1-i)*6^0.5)/16 ((3+3i)*2^0.5-( 1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((1- i)*2^0.5-(1-i)*6^0.5)/16 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((1+i)*2 ^0.5+(1+i)*6^0.5)/16 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-( 1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3+ 3i)*2^0.5-(1+i)*6^0.5)/48 ((1-i)*2^0.5-(1-i)*6^0.5)/16 ((3-3i)*2 ^0.5+(1-i)*6^0.5)/48 ((1+i)*2^0.5+(1+i)*6^0.5)/16 ((3-3i)*2^0.5+( 1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48((1-i)*2^0.5-(1-i)*6^0.5)/16 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3- 3i)*2^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3+3i)*2 ^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((1+i)*2^0.5+( 1+i)*6^0.5)/16 ((3-3i)*2^0.5+(1-i)*6^0.5)/48((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((1-i)*2^0.5-(1-i)*6^0.5)/16 ((3+ 3i)*2^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+(1-i)*6^0.5)/48 ((3-3i)*2 ^0.5+(1-i)*6^0.5)/48 ((3+3i)*2^0.5-(1+i)*6^0.5)/48 ((3-3i)*2^0.5+( 1-i)*6^0.5)/48 ((1+i)*2^0.5+(1+i)*6^0.5)/16
It can be shown that equation 2 for a sufficiently large number of time jumps or iterations N which gives the stationary time-independent solution reduces to,
W=  1/ (I-Q) . . . . .(4)
Therefore the transfer matrix W is given by,
((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840
((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840
((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840
((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840
((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840
((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840
((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840
((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5-(63-45*i)*6^0.5+32)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5-(21+15*i)*6^0.5+64)/840 ((105-35*i)*2^0.5+(21-15*i)*6^0.5+176)/840 ((105+35*i)*2^0.5+(63+45*i)*6^0.5+928)/840
And the steady-state numerical solution Eps=(W-I) . b for the vector of unit boundary conditions,
b= [1,1,1,1,1,1,1,1] T, becomes,
2^0.5+1
2^0.5+1
2^0.5+1
2^0.5+1
2^0.5+1
2^0.5+1
2^0.5+1
2^0.5+1
where all eigenvalues ​​of energy are real as expected.
[Note again the multiple appearance of 2^1/2 which has special significance in quantum mechanics.]
To be continued.
  • asked a question related to Schrodinger
Question
8 answers
how to install academic free Schrodinger desmond maestro software in Linux to run dynamic simulation?
Relevant answer
Answer
Maithra Nagaraju 1. Download the Desmond zip file in the downloads
2. then extract the file and move it to into /home/Directory through terminal
2. Then run the command sudo su in terminal
3. enter your passcode
3. then use the command chmod 777 -R /home/directory/
4. then use cd Desmond_Maestro2022.4
5. use ls command to locate the INSTALL file
6. the use command ./INSTALL
7. Enter to continue
8. then type y wherever required
9. then enter command export des=/opt/schrodinger2022-4/
10. then enter $des/maestro to run maestro'
Whenever you need to use Maestro, use steps 9 and 10 in order to start maestro desmond.
Regards
  • asked a question related to Schrodinger
Question
13 answers
In quantum mechanics, the Schrödinger equation calculated wavefunctions with a wave structure over space and changing over time. The Copenhagen interpretation, namely Born‘s interpretation states that the square modulus of the wavefunction represents the probability density function of the particle over space and time. Thus, there will be a distribution of the particle over space because we know particles are moving in the system and may favor some locations.
This is a very confusing explanation that several founders of Quantum Mechanics including Schrödinger himself, Einstein, and de Broglie have formally expressed disagreement.
I have been teaching undergraduate quantum chemistry for several years and also felt difficult to explain the probability density function why there are nodes in the solution where particles will never show up with no particular reason to avoid those places. I have been trying to come up with a different explanation of the wavefunctions with a preprint firstly posted on ChemRxiv in 4/2021. Since then I have been thinking on it and working on revisions while teaching quantum again in the past few years.
DOI: 10.26434/chemrxiv-2022-xn4t8-v17
It reaches a very surprising conclusion that the wavefunction has nothing to do with statistics as Schrödinger himself has argued many times including the famous Schrödinger’s cat thought experiment.
I recently posted the preprint in RG. Please take a read and comments are welcome. I will be teaching quantum again next semester now I have even more difficulties since I have lost beliefs on the classical interpretation.
Relevant answer
Answer
Quantum as the name implies, describes an observation we have made to the microscopic systems you have described that energy is discrete rather than continuous, which is a typical phenomenon we see in resonated wave systems at the macroscopic scale. Other than this, there should be no difference from the classical mechanics you and I have learned to describe the observations we have measured or others have measured and we trust their measurements.
  • asked a question related to Schrodinger
Question
3 answers
I am doing computational calculations on Covalent organic Frameworks using Schrodinger software. I am using PBEO-D3 theory with basis set 6-311G*. I am getting an error message. What I have to change ?
**Aborting SCF (increased accuracy is needed) consider setting nops=1 or nofail=1 in the gen section of the input file. ERROR 7009: fatal error Aborting SCF due to very large DIIS error: 1.15E+01 Error: jaguar died in program scf
Thanks in advance.
Relevant answer
Answer
Ok thank you Silpa
  • asked a question related to Schrodinger
Question
1 answer
Yes, it is entirely possible and reveals the beauty and precision of quantum mechanics when statistically understood.
We recall how the time-dependent heat equation is solved in its most general case without needing the heat PDE itself.
The question arises what are the details of similarity between the transition matrix B used in classical physics and the transition matrix Q used in quantum physics?
Relevant answer
Answer
This question is not just about classical physics, quantum physics, or mathematics, but a rigorous and comprehensive combination or incorporation of all three.
I'm sure many researchgate contributors can answer this question as well as I, if not better.
In fact, it is possible to solve the Schrödinger equation via a statistical transition matrix without needing the Schrödinger equation itself in the same way as solving the heat diffusion PDE, in his case the most general, without needing the heat equation itself.
The only requirement is the ability to imagine nature in 3D Cartesian geometry (solid geometry) and then, in a later stage, in 4D x-t unit block space.
The energy field in 4D x-t unit space has been solved in B-matrix chains and can also be solved through any other suitable statistical transition matrix.
My recommendation here is not to listen to those "HDR scientists" who dismiss the whole matter as insignificant due to their own lack of imagination and confused understanding.
While waiting for your answers or suggestions, I am preparing my own answer based on a modified B-Transition matrix (we call it Q-matrix).
Therefore, in a following answer, we provide our own numerical answers (where I assume you can personally provide answers that are adequate or better than mine) calculations of the outputs of the Schrödinger equation in an infinite potential well via the technique of the Q-matrix for the quantum transition.
  • asked a question related to Schrodinger
Question
24 answers
Complex numbers are involved almost everywhere in modern physics, but the understanding of imaginary numbers has been controversial.
In fact there is a process of acceptance of imaginary numbers in physics. For example.
1) Weyl in establishing the Gauge field theory
After the development of quantum mechanics in 1925–26, Vladimir Fock and Fritz London independently pointed out that it was necessary to replace γ by −iħ 。“Evidently, Weyl accepted the idea that γ should be imaginary, and in 1929 he published an important paper in which he explicitly defined the concept of gauge transformation in QED and showed that under such a transformation, Maxwell’s theory in quantum mechanics is invariant.”【Yang, C. N. (2014). "The conceptual origins of Maxwell’s equations and gauge theory." Physics today 67(11): 45.】
【Wu, T. T. and C. N. Yang (1975). "Concept of nonintegrable phase factors and global formulation of gauge fields." Physical Review D 12(12): 3845.】
2) Schrödinger when he established the quantum wave equation
In fact, Schrödinger rejected the concept of imaginary numbers earlier.
【Yang, C. N. (1987). Square root of minus one, complex phases and Erwin Schrödinger.】
【Kwong, C. P. (2009). "The mystery of square root of minus one in quantum mechanics, and its demystification." arXiv preprint arXiv:0912.3996.】
【Karam, R. (2020). "Schrödinger's original struggles with a complex wave function." American Journal of Physics 88(6): 433-438.】
The imaginary number here is also related to the introduction of the energy and momentum operators in quantum mechanics:
Recently @Ed Gerck published an article dedicated to complex numbers:
Our question is, is there a consistent understanding of the concept of imaginary numbers (complex numbers) in current physics? Do we need to discuss imaginary numbers and complex numbers ( dual numbers) in two separate concepts.
_______________________________________________________________________
2023-06-19 补充
On the question of complex numbers in physics, add some relevant literatures collected in recent days.
1) Jordan, T. F. (1975). "Why− i∇ is the momentum." American Journal of Physics 43(12): 1089-1093.
2)Chen, R. L. (1989). "Derivation of the real form of Schrödinger's equation for a nonconservative system and the unique relation between Re (ψ) and Im (ψ)." Journal of mathematical physics 30(1): 83-86.
3) Baylis, W. E., J. Huschilt and J. Wei (1992). "Why i?" American Journal of Physics 60(9): 788-797.
4)Baylis, W. and J. Keselica (2012). "The complex algebra of physical space: a framework for relativity." Advances in Applied Clifford Algebras 22(3): 537-561.
5)Faulkner, S. (2015). "A short note on why the imaginary unit is inherent in physics"; Researchgate
6)Faulkner, S. (2016). "How the imaginary unit is inherent in quantum indeterminacy"; Researchgate
7)Tanguay, P. (2018). "Quantum wave function realism, time, and the imaginary unit i"; Researchgate
8)Huang, C. H., Y.; Song, J. (2020). "General Quantum Theory No Axiom Presumption: I ----Quantum Mechanics and Solutions to Crisises of Origins of Both Wave-Particle Duality and the First Quantization." Preprints.org.
9)Karam, R. (2020). "Why are complex numbers needed in quantum mechanics? Some answers for the introductory level." American Journal of Physics 88(1): 39-45.
Relevant answer
Answer
Dear Chian Fan
As we all know, mathematics is a "language".
I observe that two types of persons take interest in physics, pure mathematicians and experimental physicists.
What differentiates both types is that validity of reasoning is provided by "numerical resolution" of whatever equation can be drawn from physically collected data that experimental physicists use in describing what they observe, and validity of logical derivations from sets of axiomatic postulates in the case of pure mathematicians.
One of the major difficulties in fundamental physics is the very power of mathematics as a descriptive language. If care is not taken to avoid as much as possible axiomatic postulates, an indefinite number of theories can be elaborated with full mathematical support that can always become entirely self-consistent with respect to the set of premises from which each theory is grounded. But the very self-consistency of all well thought out theories is so appealing to our rational minds that it renders very difficult the requestioning of the grounding foundations of such beautiful and intellectually satisfying structures and consequently the identification of possibly inappropriate axiomatic assumption.
Experimental physicists adapt the available math as well as they can in their attempts at mathematically describing what they observe from the data they collected – of which i never is an element, while pure mathematicians explain what logically comes out of whatever sets of axiomatic premises that they chose to underlie their worldview.
From what I understand, √-1 just happened to be part of the mathematical toolset that Schrödinger had at his disposal in trying to mathematized how to account for the stationary resonance state that de Broglie had discovered that the electron is captive of when stabilized in the hydrogen atom ground state, a resonance frequency to which those of all other metastable orbitals of the hydrogen atom and emitted bremsstrahlung photons are related by the well established sequence of integers that de Broglie provided in his 1924 thesis.
Best Regards, André
  • asked a question related to Schrodinger
Question
1 answer
Heighenberg Uncertainty Principle has been found applicable only applicable to atomic systems while Quantum Theory of Uncertainty Principle of Integral Space has been foundle suitable for all the systems of Universe and Nature.Thats why it has been pronounced as "Quantum Theory of Everything" which was a dream of many pioneers including Albert Einstein ,Neels Bohr, Schrodinger,Tesla etc.
For details following recent three research papers have been uploaded.
Relevant answer
Answer
It has been also observed that Heighenberg Uncertainty Principle is deriveable from Quantum Theory of Uncertainty Principle of Integral Space.Not only this but other Pioneer's theories have been also derived from present Integral Space Quantum Theory.
  • asked a question related to Schrodinger