The Klein-Gordon equation with a generalized Hulthen potential in D-dimensions

TL;DR

This paper derives approximate bound state solutions for the Klein-Gordon equation with a generalized Hulthen potential in D-dimensions, providing energy eigenvalues and eigenfunctions expressed via hypergeometric polynomials.

Contribution

It introduces an approximation method for the centrifugal term and extends solutions to D-dimensions for Hulthen-type potentials.

Findings

Derived explicit energy eigenvalues and eigenfunctions

Extended solutions to D-dimensional space

Provided analytical expressions in terms of hypergeometric polynomials

Abstract

An approximate solution of the Klein-Gordon equation for the general Hulth\'en-type potentials in $D$-dimensions within the framework of an approximation to the centrifugal term is obtained. The bound state energy eigenvalues and the normalized eigenfunctions are obtained in terms of hypergeometric polynomials.