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Chinese Physics B

The nonrelativistic oscillator strength of a hyperbolic-type potential

HASSAN HASSANABADI, S. Zarrinkamar, Bentol Hoda Yazarloo

Published Jun 1, 2013• 11 citations
Publisher

Abstract

We consider the D -dimensional Schrödinger equation under the hyperbolic potential V 0 (1 − coth(α r )) + V 1 (1 − coth(α r )) 2 . Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.

DOI
10.1088/1674-1056/22/6/060202

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We consider the D -dimensional Schrödinger equation under the hyperbolic potential V 0 (1 − coth(α r )) + V 1 (1 − coth(α r )) 2 . Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.
The Schrödinger equation under the ManningRosen potential is solved in arbitrary dimension via the quantum mechanical idea of supersymmetry.The Pekeris approximation is used to overcome the inconsistency of the potential with the centrifugal term.Comments on the energy eigenvalue behavior versus dimension are included.The inter-dimensional degeneracy for various orbital quantum number l and dimensions D are studied.The expectation values of some physical parameters are reported via the FeynmanHellmann theorem.
The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials become exactly and quasi-exactly solvable potentials of nonrelativistic quantum mechanics when they are transformed into a Schrödinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics.