Analytical approximations to the l-wave solutions of the Klein–Gordon equation with position-dependent mass for mixed vector and scalar Hulthén-type potentials by using SUSYQM approach

In this paper, we investigate the approximate bound states solutions of Klein–Gordon equation with position-dependent mass for scalar and vector central Hulthén-type potentials by applying an approximation scheme to deal with the centrifugal potential for any l -states. The supersymmetric quantum mechanics (SUSYQM) and shape invariance approaches are used in the calculations. We obtain straightforwardly the relativistic energies and their corresponding normalized wavefunctions, expressed in terms of Jacobi polynomials. Special cases of interest of this problem are also deduced and it is found that our results are in good agreement with those obtained in the literature.