Approximate Analytical Solutions of the Effective Mass Dirac Equation for the generalized Hulthen Potential with any kappa-Value

TL;DR

This paper presents approximate analytical solutions to the Dirac equation with position-dependent mass for the generalized Hulthén potential across all kappa-values, using a coordinate transformation and the Nikiforov-Uvarov method.

Contribution

It introduces a novel approach to solving the Dirac equation with position-dependent mass for the generalized Hulthén potential for any spin-orbit quantum number.

Findings

Derived energy eigenvalues and wave functions for the system.

Results agree well with existing literature for constant mass case.

Numerical solutions validate the analytical approach.

Abstract

The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulth\'{e}n potential with any spin-orbit quantum number $\kappa$. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schr\"{o}dinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.