Approximate l-State Solutions of the Klein-Gordon Equation for Modified Woods-Saxon Potential With Position Dependent Mass

TL;DR

This paper develops an analytical method to solve the Klein-Gordon equation with a position-dependent mass for the modified Woods-Saxon potential, providing energy eigenvalues and eigenfunctions, and compares with constant mass cases.

Contribution

It introduces a new approximation scheme for the centrifugal potential term in the Klein-Gordon equation with spatially dependent mass.

Findings

Derived energy eigenvalues for the potential with position-dependent mass.

Obtained normalized eigenfunctions for the system.

Validated the approximation scheme by comparing with constant mass solutions.

Abstract

The radial part of the Klein-Gordon equation for the generalized Woods-Saxon potential is solved by using the Nikiforov-Uvarov method in the case of spatially dependent mass within the new approximation scheme to the centrifugal potential term. The energy eigenvalues and corresponding normalized eigenfunctions are computed. The solutions in the case of constant mass are also studied to check out the consistency of our new approximation scheme.