Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass

TL;DR

This paper solves the Klein-Gordon equation with a Woods-Saxon potential and position-dependent mass using the Nikiforov-Uvarov method, providing energy eigenvalues and eigenfunctions, including the constant mass case.

Contribution

It introduces an analytical solution for the Klein-Gordon equation with position-dependent mass in a Woods-Saxon potential using the Nikiforov-Uvarov method.

Findings

Energy eigenvalues computed for position-dependent mass

Eigenfunctions derived analytically

Results extended to constant mass case

Abstract

The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.