Approximate Pseudospin and Spin Solutions of the Dirac Equation for a Class of Exponential Potentials

TL;DR

This paper solves the Dirac equation for specific exponential potentials under spin and pseudospin symmetry, deriving energy eigenvalues and wave functions using an approximation and the Nikiforov-Uvarov method.

Contribution

It introduces an approximation for the centrifugal term and applies the Nikiforov-Uvarov method to find solutions for non s-waves in exponential potentials.

Findings

Derived energy eigenvalue equations for the potentials.

Obtained explicit wave functions for the solutions.

Extended solutions to non s-waves with an exponential approximation.

Abstract

Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $\kappa$ in the case of spin and pseudospin symmetry, respectively. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations, and the corresponding wave functions are obtained by using the generalization of the Nikiforov-Uvarov method.