Approximate Analytical Solutions of the Effective Mass Klein-Gordon Equation for Yukawa potential

TL;DR

This paper derives approximate analytical solutions for the Klein-Gordon equation with Yukawa potential, considering position-dependent mass and using the Nikiforov-Uvarov method, providing insights into energy levels and wave functions.

Contribution

It introduces a new approximation approach for solving the Klein-Gordon equation with Yukawa potential for arbitrary states with position-dependent mass.

Findings

Energy eigenvalues are obtained analytically.

The effect of screening parameter on energy levels is analyzed.

Results agree with existing literature in the constant mass and nonrelativistic limits.

Abstract

The analytical solutions of the Klein-Gordon equation with the Yukawa potential is presented within the framework of an approximation to the centrifugal potential for any arbitrary state with the position-dependent mass using the parametric Nikiforov-Uvarov method. The energy eigenvalues and the corresponding wave function have been obtained. The energy for both the scalar potential and vector potential as well as the effect of the screening parameter on each of the energy for scalar potential and vector potential are investigated in detail. The nonrelativistic limit is obtained and numerical results are computed. It is found that our results for the constant mass and that of the nonrelativistic limit are in good agreement with the one in the literature.