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# Schrodinger - Science topic

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Questions related to Schrodinger

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?

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?

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

If ever confirmed, the applicative potential would be tremendous...

I refer here to Grinwald's publication:

- P. M. Grinwald, "
**Schrödinger’s Equation as a Consequence of the Central Limit Theorem Without Assuming Prior Physical Laws**", 2022 - https://www.researchgate.net/publication/360150783_Schrodinger%27s_Equation_as_a_Consequence_of_the_Central_Limit_Theorem_Without_Assuming_Prior_Physical_Laws

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.

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?

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.

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)

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.

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.

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.

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].

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.

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.

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.

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.

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.

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.

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!

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?

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?

i have performed simulation in two steps and I wasn't able to merge the energy files. Provide help

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.

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

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).

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.

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.

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

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.

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.

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?

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.

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?

Also, is there a way to convert SMILES into IUPAC or common name of the compound?

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.

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.

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.

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?

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?

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?

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?

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?

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.

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?

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.

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

Schrödinger is one of the most prominent software for molecular docking. Is MOE also reliable for ligand docking.

regards,

Pratik

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?

Hello, do you know Schrödinger's equation is valid for all mediums in which a particle moves, such as glass, water, and air...? Thanks.

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?

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.

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.

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?

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.

how to install academic free Schrodinger desmond maestro software in Linux to run dynamic simulation?

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.

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.

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?

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.

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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.

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.