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

Abstract

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solution within the framework of the position-dependent effective mass radial Klein–Gordon equation with the scalar and vector Hulthén 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 the literature.