Exact Klein-Gordon equation with spatially-dependent masses for unequal scalar-vector Coulomb-like potentials

TL;DR

This paper derives exact solutions for the Klein-Gordon equation with spatially dependent masses and Coulomb-like potentials, revealing how mass variation influences bound state energies in relativistic quantum systems.

Contribution

It provides exact bound state solutions for the Klein-Gordon equation with spatially dependent masses and Coulomb-like potentials using the Nikiforov-Uvarov method, including various potential mixing scenarios.

Findings

Energy eigenvalues depend on mass distribution and potential mixing.

Exact wave functions are obtained for different potential cases.

The approach extends solutions to variable mass relativistic particles.

Abstract

We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3+1)-dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are directly proportional and inversely proportional to the distance from force center. The exact bound state energy eigenvalues and the corresponding wave functions of the Klein-Gordon equation for mixed scalar-vector and pure scalar Coulomb-like field potentials are obtained by means of the Nikiforov-Uvarov (NU) method. The energy spectrum is discussed for different scalar-vector potential mixing cases and also for constant mass case.