Solutions of Dirac Equation for Symmetric Generalized Woods-Saxon Potential by the Hypergeometric Method

TL;DR

This paper presents an approximate solution to the Dirac equation with a generalized Woods-Saxon potential using the hypergeometric method, focusing on pseudospin symmetry and position-dependent mass backgrounds.

Contribution

It introduces a novel application of the Nikiforov-Uvarov method to solve the Dirac equation with a generalized Woods-Saxon potential under pseudospin symmetry.

Findings

Derived energy eigenvalues for the system.

Obtained explicit wave functions.

Extended solutions to position-dependent mass scenarios.

Abstract

The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into a Schr\"{o}dinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.