Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

TL;DR

This paper introduces a new approximation scheme for solving the Klein-Gordon equation with position-dependent mass and Hulthén potentials, providing quasi-exact analytical solutions for bound states in arbitrary dimensions.

Contribution

It develops a novel approximation for the centrifugal term, enabling closed-form solutions for the Klein-Gordon equation with scalar and vector Hulthén potentials in any dimension.

Findings

Derived relativistic energy levels and eigenfunctions in closed form.

Solutions reduce to known cases for constant mass and s-wave.

Applicable to various screening parameters and dimensions.

Abstract

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulth\'{e}n potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.