Bound state solutions of the generalized shifted Hulthen potential

TL;DR

This paper derives approximate solutions for the Schrödinger equation with the generalized shifted Hulthen potential in arbitrary dimensions, computing energy eigenvalues and eigenfunctions, and validating results against known potentials and literature.

Contribution

It introduces a new approximate solution method for the Schrödinger equation with the generalized shifted Hulthen potential using the Nikiforov-Uvarov approach, including special cases and extensions.

Findings

Numerical eigenvalues agree across approximation schemes.

Derived energy expressions match existing literature for special cases.

Extended solutions to s-wave cases for Hulthen and Woods-Saxon potentials.

Abstract

In this study, we obtain an approximate solution of the Schrodinger equation in arbitrary dimensions for the generalized shifted Hulthen potential model within the framework of the Nikiforov-Uvarov method. The bound state energy eigenvalues were computed and the corresponding eigenfunction was also obtained. It is found that the numerical eigenvalues were in good agreement for all three approximations scheme used. Special cases were considered when the potential parameters were altered, resulting into Hulthen Potential and Woods-Saxon Potential respectively. Their energy eigenvalues expressions agreed with the already existing literatures. A straightforward extension to the s-wave case for Hulthen potential and Woods-Saxon Potential cases are also presented.