Approximate Analytical Solutions of the Klein-Gordon Equation for Hulthen Potential with Position-Dependent Mass

TL;DR

This paper derives approximate analytical solutions for the Klein-Gordon equation with a Hulthén potential and position-dependent mass, using the Nikiforov-Uvarov method, extending previous constant-mass results.

Contribution

It introduces an approximate analytical approach for solving the Klein-Gordon equation with position-dependent mass and Hulthén potential for any angular momentum.

Findings

Results agree with known constant-mass solutions

Energy eigenvalues and wave functions obtained

Method applicable to various quantum states

Abstract

The Klein-Gordon equation is solved approximately for the Hulth\'{e}n potential for any angular momentum quantum number $\ell$ with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a Schr\"{o}dinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get an energy eigenvalue and and the wave functions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.