arXiv subjects

K. D. Sen

Publications and source records attributed to K. D. Sen.

15 recordsLinked to original sources

arXiv2018

Exact normalized eigenfunctions for general deformed Hulthén potentials

The exact solutions of Schrödinger's equation with the deformed Hulthén potential $V_q(x)=-{μ\, e^{-δ\,x }}/({1-q\,e^{-δ\,x}}),~ δ,μ, q>0$ are given, along with a closed--form formula for the normalization constants of the eigenfunctions for arbitrary $q>0$. The Crum-Darboux transformation is then used to derive the corresponding exact solutions for the extended Hulthén potentials $V(x)= -{μ\, e^{-δ\,x }}/({1-q\,e^{-δ\,x}})+ {q\,j(j+1)\, e^{-δ\,x }}/({1-q\,e^{-δ\,x}})^2, j=0,1,2,\dots.$ A general formula for the new normalization condition is also provided.

math-ph↗

arXiv2018

Complexity Study of a Single Particle Under q-Deformed Potentials

We have studied the variation of the position space statistical complexity measure defined by López-Ruiz, Mancini, and Calbet such as the product of exponential of the Shannon information entropy and the disequilibrium by using the 1D-normalized probability densities derived from solutions of the Schrödinger equation corresponding to the q-deformed harmonic oscillator and q-deformed Morse potentials. An analysis of the numerical results in terms of Shannon information entropy, disequilibrium and complexity measure are presented. In q-deformed harmonic oscillator, q-dependence of the complexity shows a minimum point for all excited energy levels. In the case of q-deformed Morse Potential, complexity decreases with increasing $q$ for the investigated diatomic molecules.

quant-ph↗

arXiv2014

Soft and hard confinement of a two-electron quantum system

A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius $R.$ When hard confinement is present the oscillators can be switched off. Exact analytical solutions are found for special parameter sets, and highly accurate numerical solutions (18 decimal places) are obtained for general cases. Some interesting degeneracy questions are discussed at length.

math-ph↗

arXiv2014

Position and momentum information-theoretic measures of the pseudoharmonic potential

In this study, the information-theoretic measures in both the position and momentum spaces for the pseudoharmonic potential using Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy and Onicescu information energy are investigated analytically and numerically. The results obtained are applied to some diatomic molecules. The Renyi and Tsallis entropies are analytically obtained in position space using Srivastava-Niukkanen linearization formula in terms of the Lauricella hypergeometric function. Also they are obtained in the momentum space in terms of the multivariate Bell polynomials of Combinatorics. We observed that the Fisher information increases with $n$ in both the position and momentum spaces, but decreases with $\ell$ for all the diatomic molecules considered. The Shannon entropy also increases with increasing $n$ in the position space and decreases with increasing $\ell$. The variations of the Renyi and Tsallis entropies with $\ell$ are also discussed. The exact and numerical values of the Onicescu information energy are also obtained, after which the ratio of information-theoretic impetuses to lengths for Fisher, Shannon and Renyi are obtained.

quant-ph↗

arXiv2014

Quantum Information Entropies for the $\ell$-state Pöschl-Teller-type potential

In this study, we obtained the position-momentum uncertainties and some uncertainty relations for the Pöschl-Teller-type potential for any $\ell$. The radial expectation values of $r^{-2}$, $r^{2}$ and $p^{2}$ are obtained from which the Heisenberg Uncertainty principle holds for the potential model under consideration. The Fisher information is then obtained and it is observed that the Fisher-information-based uncertainty relation and the Cramer-Rao inequality hold for this even power potential. Some numerical and graphical results are displayed.

quant-ph↗

arXiv2011

Spectroscopic Studies of Some Diatomic Molecules using Spectrum Generating Algebra Approach

For arbitrary values n and l quantum numbers, we present the solutions of the 3-dimensional Schrodinger wave equation with the pseudoharmonic potential via SU(1,1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r2 and r d/dr are obtained (in a closed form) directly from the creation and annihilation operators. In addition, the expectation values of r2 and p2 and the Heisenberg Uncertainty Products (HUP) for set of diatomic molecules (O2, I2, N2, H2, CO, NO, HCl, CH, LiH, ScH, TiH, VH, CrH, MnH, TiC, NiC, ScN, ScF, Ar2) for arbitrary values of n and l quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.

physics.chem-ph↗

arXiv2011

Spectral characteristics for a spherically confined -1/r + br^2 potential

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.

math-ph↗

arXiv2010

Electron correlation energy in confined two-electron systems

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05 - 10 a0. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z > 1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy.

physics.atom-ph↗

arXiv2009

Soft-core Coulomb potentials and Heun's differential equation

Schroedinger's equation with the attractive potential V(r) = -Z/(r^q+ b^q)^(1/q), Z > 0, b > 0, q >= 1, is shown, for general values of the parameters Z and b, to be reducible to the confluent Heun equation in the case q=1, and to the generalized Heun equation in case q=2. In a formulation with correct asymptotics, the eigenstates are specified a priori up to an unknown factor. In certain special cases this factor becomes a polynomial. The Asymptotic Iteration Method is used either to find the polynomial factor and the associated eigenvalue explicitly, or to construct accurate approximations for them. Detail solutions for both cases are provided.

math-ph↗

arXiv2009

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+β^q)^{\frac{1}{q}}}, with the parameters Z>0, β>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{ν\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{ν\ell} and corresponding wave functions, expressed in terms of Z and β. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(ν,\ell),(ν',\ell')], is given by the condition ν'\geq (ν+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.

math-ph↗

arXiv2009

Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields

The scaling properties of various composite information-theoretic measures (Shannon and Rényi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in position and momentum spaces for the non-relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields. Such measures are found to be invariant at the fixed values of the scaling parameters given by $s_1 = B \hbar^3(4πε_0)^2 / (Z^2m^2e^3)$ and $s_2 = F \hbar^4(4πε_0)^3 / (Z^3e^5m^2)$. Numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity. Physical significance of the resulting scaling behaviour is discussed.

physics.chem-ph↗

arXiv2009

Lower Bound for LMC complexity measure

Lower bound for the shape complexity measure of López-Ruiz-Mancini-Calbet (LMC), $C_{LMC}$, is derived. Analytical relations for simple examples of the harmonic oscillator, the hydrogen atom and two-electron 'entangled artificial' atom proposed by Moshinsky are derived. Several numerical examples of the spherically confined model systems are presented as the test cases. For the homogeneous potential, $C_{LMC}$ is found to be independent of the parameters in the potential which is not the case for the non-homogeneous potentials.

physics.chem-ph↗

arXiv2009

Relativistic effects on information measures for hydrogen-like atoms

Position and momentum information measures are evaluated for the ground state of the \emph{relativistic} hydrogen-like atoms. Consequences of the fact that the radial momentum operator is not self-adjoint are explicitly studied, exhibiting fundamental shortcomings of the conventional uncertainty measures in terms of the radial position and momentum variances. The Shannon and Rényi entropies, the Fisher information measure, as well as several related information measures, are considered as viable alternatives. Detailed results on the onset of relativistic effects for low nuclear charges, and on the extreme relativistic limit, are presented. The relativistic position density decays exponentially at large $r$, but is singular at the origin. Correspondingly, the momentum density decays as an inverse power of $p$. Both features yield divergent Rényi entropies away from a finite vicinity of the Shannon entropy. While the position space information measures can be evaluated analytically for both the nonrelativistic and the relativistic hydrogen atom, this is not the case for the relativistic momentum space. Some of the results allow interesting insight into the significance of recently evaluated Dirac-Fock vs. Hartree-Fock complexity measures for many-electron neutral atoms.

physics.atom-ph↗

arXiv2006

Net Fisher information measure versus ionization potential and dipole polarizability in atoms

The net Fisher information measure, defined as the product of position and momentum Fisher information measures and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z=1-102, is found to correlate well with the inverse of the experimental ionization potential. Strong direct correlations of the net Fisher information are also reported for the static dipole polarizability of atoms with Z=1-88. The complexity measure, defined as the ratio of the net Onicescu information measure and net Fisher information, exhibits clearly marked regions corresponding to the periodicity of the atomic shell structure. The reported correlations highlight the need for using the net information measures in addition to either the position or momentum space analogues. With reference to the correlation of the experimental properties considered here, the net Fisher information measure is found to be superior than the net Shannon information entropy.

quant-ph↗

arXiv2006

Spherically confined isotropic harmonic oscillator

The generalized pseudospectral Legendre method is used to carry out accurate calculations of eigenvalues of the spherically confined isotropic harmonic oscillator with impenetrable boundaries. The energy of the confined state is found to be equal to that of the unconfined state when the radius of confinement is suitably chosen as the location of the radial nodes in the unconfined state. This incidental degeneracy condition is numerically shown to be valid in general. Further, the full set of pairs of confined states defined by the quantum numbers [(n+1, \ell) ; (n, \ell+2)], n = 1,2,.., and with the radius of confinement {(2 \ell +3)/2}^{1/2} a.u., which represents the single node in the unconfined (1, \ell) state, is found to display a constant energy level separation exactly given by twice the oscillator frequency. The results of similar numerical studies on the confined Davidson oscillator with impenetrable boundary as well as the confined isotropic harmonic oscillator with finite potential barrier are also reported .The significance of the numerical results are discussed.

quant-ph↗