Effective Mass Dirac-Morse Problem with any kappa-value

TL;DR

This paper solves the Dirac-Morse problem with position-dependent mass for any kappa-value, providing analytical energy eigenvalues and wave functions using the Nikiforov-Uvarov method, and compares with constant-mass cases.

Contribution

It introduces a generalized analytical approach to the Dirac-Morse problem with position-dependent mass for arbitrary kappa-values, extending previous methods.

Findings

Derived explicit energy eigenvalues for the Dirac-Morse problem with position-dependent mass.

Obtained wave functions corresponding to the energy eigenvalues.

Compared results with constant-mass cases for pseudospin and spin symmetries.

Abstract

The Dirac-Morse problem are investigated within the framework of an approximation to the term proportional to $1/r^2$ in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov-Uvarov method for any $\kappa$-value. It is also studied the approximate energy eigenvalues, and corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.