Approximate l-State Solutions of a Spin-0 Particle for Woods-Saxon Potential

TL;DR

This paper derives approximate solutions for a spin-0 particle in the Woods-Saxon potential using the Klein-Gordon and Schrödinger equations, employing the Nikiforov-Uvarov method to find bound states and eigenfunctions.

Contribution

It introduces an approximation method to solve the radial Klein-Gordon equation with Woods-Saxon potential, providing consistent solutions for bound states and eigenfunctions.

Findings

Bound state energies computed for Woods-Saxon potential

Eigenfunctions normalized and consistent with previous results

Solutions applicable to both Klein-Gordon and Schrödinger equations

Abstract

The radial part of Klein-Gordon equation is solved for the Woods-Saxon potential within the framework of an approximation to the centrifugal barrier. The bound states and the corresponding normalized eigenfunctions of the Woods-Saxon potential are computed by using the Nikiforov-Uvarov method. The results are consistent with the ones obtained in the case of generalized Woods-Saxon potential. The solutions of the Schr\"{o}dinger equation by using the same approximation are also studied as a special case, and obtained the consistent results with the ones obtained before.