Neetik Mukherjee

Neetik Mukherjee
Indian Institute of Science Education and Research Kolkata · Department of Chemical Sciences

PhD
correlation effect in confined quantum systems.

About

32
Publications
3,391
Reads
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251
Citations
Additional affiliations
March 2019 - present
Indian Institute of Science Education and Research Kolkata
Position
  • Research Associate
March 2019 - February 2022
Indian Institute of Science Education and Research Kolkata
Position
  • Research Associate
September 2016 - September 2018
Indian Institute of Science Education and Research Kolkata
Position
  • DST-SERB NATIONAL POST-DOCTORAL FELLOW

Publications

Publications (32)
Article
Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shan-non entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenval-ues and eigenvectors of this system are obtained through a variation-induced exact diagonalization procedure. The information entro...
Article
Full-text available
Perturbation theory based model can be used to locate the quasi-degeneracy in an arbitrary double well potential. In this work, unconstrained optimisation has been done using Simulated Annealing to calculate the energy spectrum of double well potential. Using this calculation the author has studied the effect of a Gaussian perturbation on single an...
Article
In this work a new state dependent Uncertainty Principle between kinetic and potential energy is formulated using Time independent Schrödinger Equation and Correspondence Principle. Validity of the above said Uncertainty Principle is also demonstrated by linear variational calculation of a one-dimensional model potential. An objective function is a...
Article
Quantum mechanical variation principle in the form of energy minimization is applicable only to ground states of systems, or, at best, states of lowest energies of given symmetries, provided the symmetry information is embedded in chosen trial functions. Thus, for bound quantum states with specified choices of trial functions involving nonlinear pa...
Article
In this paper, we seek to design optimum pulses for selective target excitation to specified excited levels. We test our proposed idea for vibrational excitation in systems modelled by the Morse potential, using the time dependent Fourier grid Hamiltonian technique and the simulated annealing method.
Article
Full-text available
Multipole oscillator strength (f(k)) acts as a foundation in estimating multipole polarizability (α(k)i) in a quantum system. Moreover, a knowledge of f(k) as well as α(k)i under extreme pressure may be treated as the benchmark in high pressure spectroscopy. Further, an investigation of rate of change of these quantities and transition moment integ...
Preprint
Full-text available
The behavior of H-like ions embedded in astrophysical plasmas in the form of \emph{dense, strongly and weakly coupled} plasmas are investigated. In these, the increase and decrease in temperature is impacted with a change in confinement radius $(r_{c})$. Two independent and generalized scaling ideas have been applied to modulate the effect of plasm...
Article
Full-text available
Shell-confined atoms can serve as a generalized model to explain both the free and confined conditions. In this scenario, an atom is trapped inside two concentric spheres of inner (Ra) and outer (Rb) radii. The choice of Ra and Rb renders four different quantum-mechanical systems. In hydrogenic atoms, they are termed (i) the free hydrogen atom (FHA...
Article
The behavior of H-like ions embedded in astrophysical plasmas in the form of dense, strongly and weakly coupled plasmas is investigated. In these, the increase and decrease in temperature are impacted by a change in confinement radius rc. Two independent and generalized scaling ideas have been applied to modulate the effect of the plasma-screening...
Preprint
Full-text available
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology,etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable...
Article
Full-text available
Ground and excited states of a confined negative hydrogen ion have been pursued under Kohn–Sham density functional approach by invoking a physically motivated work-function-based exchange potential. The exchange-only results are of near Hartree–Fock quality. Local parameterized Wigner-type, and gradient- and Laplacian-dependent non-local Lee–Yang–P...
Preprint
Full-text available
Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile for such systems has not yet been investigated. Here we construct the Compton profile (CP) for a H atom radially confined inside a \emph{hard} spherical enclosure, as well as in \emph{free condition}. Some exact analytical relations...
Article
Full-text available
Over the past two decades, constrained quantum systems have arisen to be a field of considerable importance in physical, chemical and biological sciences. In this work, we have investigated the behavior of a confined H atom inside a harmonic environment: V (r) = − 1 r + r rc 2. The eigenvalue equation is solved using a generalized Legendre pseudosp...
Article
Full-text available
Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile for such systems has not yet been investigated. Here we construct the Compton profile (CP) for a H atom radially confined inside a hard spherical enclosure, as well as in free condition. Some exact analytical relations for the CP's o...
Book
This book gathers state-of-the-art advances on harmonic oscillators including their types, functions, and applications. In Chapter 1, Neetik and Amlan have discussed the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of ph...
Article
Full-text available
Various well-known statistical measures like López-Ruiz, Mancini, Calbet (LMC) and Fisher–Shannon complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position (r) and momentum (p) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with Rényi entropy (R) is invoked here. The...
Preprint
Full-text available
Various well-known statistical measures like \emph{L\'opez-Ruiz, Mancini, Calbet} (LMC) and \emph{Fisher-Shannon} complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position ($r$) and momentum ($p$) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with R\'enyi entropy ($...
Article
Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavity has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like equation in terms of mean square and expectation values of potential and kinetic energy operators. It appears to be a...
Article
Shannon entropy (S), Fisher information (I) and a measure equivalent to Fisher-Shannon complexity (CIS) of a ro-vibrational state of diatomic molecules (O2, O+ 2 , NO, NO+) with generalized Kratzer potential is analyzed. Exact analytical expression of Ir is derived for the arbitrary state, whereas the same could be done for Ip with {n, ℓ,m = 0} sta...
Article
Relative Fisher information (IR) was pursued for 1D quantum harmonic oscillator (QHO), 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both r and p spaces. In 1D case, the n = 0 state is chosen as reference, whereas for a central potential, the respective circular (corresponding to lowest radial quantum number nr) state of a g...
Article
Information based uncertainty measures like Rényi entropy (R), Shannon entropy (S) and On-icescu energy (E) (in both position and momentum space) are employed to understand the influence of radial confinement in isotropic harmonic oscillator. The transformation of Hamiltonian in to a dimensionless form gives an idea of the composite effect of oscil...
Article
Full-text available
Fisher information (I) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate r and p spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as well as CHO and respective free harmonic oscillator (FHO) is pursued with respect to energy spectrum and I. This reveal...
Article
Full-text available
Rényi entropy (R), Tsallis entropy (T), Shannon entropy (S), and Onicescu energy (E) are studied in a spherically confined H atom (CHA), in conjugate space, with special emphasis on non-zero l states. Representative calculations are done by employing exact analytical wave functions in r space. Accurate p space-wave functions are generated numerical...
Article
Full-text available
Shannon entropy ($S$), R{\'e}nyi entropy ($R$), Tsallis entropy ($T$), Fisher information ($I$) and Onicescu energy ($E$) have been explored extensively in both \emph{free} H atom (FHA) and \emph{confined} H atom (CHA). For a given quantum state, accurate results are presented by employing respective \emph{exact} analytical wave functions in $r$ sp...
Article
Full-text available
Fisher information (I) is investigated for confined hydrogen atom (CHA)-like systems in conjugate $r$ and $p$ spaces. A comparative study between CHA and free H atom (with respect to $I$) is pursued. In many aspects, inferences in CHA are significantly different from free counterpart; that includes its dependence on $n, l, m$. The role of atomic nu...
Article
Full-text available
Several well-known statistical measures similar to LMC and Fisher-Shannon complexity have been computed for confined hydrogen atom in both position (r) and momentum (p) spaces. Further, a more generalized form of these quantities with Rényi entropy (R) is explored here. The role of scaling parameter in the exponential part is also pursued. R is eva...
Article
Full-text available
Information-based uncertainty measures like Shannon entropy, Onicescu energy and Fisher information (in position and momentum space) are employed to understand the effect of symmetric and asymmetric confinement in a quantum harmonic oscillator. Also, the transformation of the Hamiltonian into a dimensionless form gives an idea of the composite effe...
Article
Full-text available
Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phase-space area, are utilized to explain the contrasting effect of localization-delocalization and role of asymmetric term...
Article
Perturbation theory based model can be used to locate the quasi-degeneracy in an arbitrary double well potential. This method, extensively explain the effect of the coupling term on pair of states called quasi-degenerate. This model helps us to calculate the energy of the pair of quasi-degenerate states using appreciably small basis. Dispersion equ...
Article
Precise supersymmetric partner potentials can be generated for exactly solvable problems of the stationary Schrödinger equation. Construction of isospectral potential is not always possible for exactly solvable systems. This is a restriction, as most problems are not exactly solvable. Employment of mirror-image property can help to construct an exa...
Article
Precise supersymmetric (SUSY) partner potentials can be generated only for exactly solvable problems of the stationary Schrödinger equation. This is a severe restriction, as most problems are not amenable to exact solutions. We employ here a linear variational strategy to explicitly construct approximate SUSY partners of a few common, not exactly s...

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Projects

Project (1)
Archived project
To calculate time independent and time dependent information entropies for confined potentials