Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential

TL;DR

This paper derives analytical solutions for the Klein-Gordon equation with the Woods-Saxon potential for any angular momentum state, providing explicit energy eigenvalues and eigenfunctions using the Nikiforov-Uvarov method.

Contribution

It introduces a method to obtain exact bound state solutions of the Klein-Gordon equation with the Woods-Saxon potential for all l-states, including the non-relativistic limit.

Findings

Exact energy eigenvalues for various quantum numbers n and l

Explicit eigenfunctions corresponding to these energy levels

Non-relativistic limit of the energy spectrum obtained

Abstract

The radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any $l$ states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers $n$ and $l$. The non-relativistic limit of the bound state energy spectrum was also found.