Approximate Solution of the effective mass Klein-Gordon Equation for the Hulthen Potential with any Angular Momentum

TL;DR

This paper presents an approximate analytical solution to the effective mass Klein-Gordon equation with the Hulthen potential, using the Nikiforov-Uvarov method, for any angular momentum state, including the constant mass case.

Contribution

It introduces an approximation technique for the centrifugal potential and applies the Nikiforov-Uvarov method to obtain energy spectra and eigenfunctions for the Hulthen potential.

Findings

Derived energy eigenvalues for various angular momenta

Obtained eigenfunctions corresponding to the energy levels

Extended solutions to the constant mass scenario

Abstract

The radial part of the effective mass Klein-Gordon equation for the Hulthen potential is solved by making an approximation to the centrifugal potential. The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the corresponding eigenfunctions are computed. Results are also given for the case of constant mass.