ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL

Bako M Bitrus,U Wadata,C M Nwabueze,E S Eyube

doi:10.33003/fjs-2021-0501-614

Bako M Bitrus, U Wadata + Show 2 more

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https://doi.org/10.33003/fjs-2021-0501-614

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Abstract

In this paper, concept of supersymmetric quantum mechanics has been employed to derive expression for bound state energy eigenvalues of the Tietz-Hulthén potential, the corresponding equation for normalized radial eigenfunctions were deduced by ansatz solution technique. In dealing with the centrifugal term of the effective potential of the Schrödinger equation, a Pekeris-like approximation recipe is considered. By means of the expression for bound state energy eigenvalues and radial eigenfunctions, equations for expectation values of inverse separation-squared and kinetic energy of the Tietz-Hulthén potential were obtained from the Hellmann-Feynman theorem. Numerical values of bound state energy eigenvalues and expectation values of inverse separation-squared and kinetic energy the Tietz-Hulthén potential were computed at arbitrary principal and angular momentum quantum numbers. Results obtained for computed energy eigenvalues of Tietz-Hulthén potential corresponding to Z = 0 and V0 = 0 are in excellent agreement with available literature data for Tietz and Hulthén potentials respectively. Studies have also revealed that increase in parameter Z results in monotonic increase in the mean kinetic energy of the system. The results obtained in this work may find suitable applications in areas of physics such as: atomic physics, chemical physics, nuclear physics and solid state physics

Highlights

Potential energy functions are relevant in quantum mechanics because they provide a means of representing the interaction between a physical object and its neighborhood (Yanar et al, 2021)
This work aims at obtaining the energy spectrum and some useful expectation values of a proposed Tietz-Hulthén potential, the Tietz-Hulthén potential is a combination of the Hulthén potential plus Tietz potential expressed as
In order to confirm the validity of the equation for energy spectrum of the Tietz-Hulthén potential derived in this work, it is observed that by letting V0 = 0, equation (1) is reduced to Hulthén potential energy function (Varshni, 1990)

Summary

Introduction

Potential energy functions (or more potential) are relevant in quantum mechanics because they provide a means of representing the interaction between a physical object and its neighborhood (Yanar et al, 2021). All the necessary information regarding a quantum mechanical system can be obtained from wave functions representing the system under investigation (Tsaur and Wang, 2014; Eyube et al, 2019a). Different solution methods of the Schrödinger and other wave equations have been advocated in the literature, among which include: supersymmetric quantum mechanics (Hassanabadi et al, 2013b), Nikiforov-Uvarov method and its parametric form (Nikoofard et al, 2013), exact and proper quantization rule (Eyube et al, 2020c; Eyube et al, 2021b), ansatz solution method (Chen and Jia, 2009) and asymptotic iteration method (Sous, 2019) Quite a number of potential energy functions have been used to solve the Schrödinger equation, one of such potential models is the Hulthén potential.

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