Approximate relativistic bound state solutions of the Tietz-Hua rotating oscillator for any -state

TL;DR

This paper derives approximate analytical solutions to the Dirac equation with the Tietz-Hua potential, providing energy levels and wave functions for relativistic particles under spin and pseudo-spin symmetry, including special cases.

Contribution

It introduces a novel application of the Nikiforov-Uvarov method to solve the Dirac equation with the Tietz-Hua potential for arbitrary spin-orbit quantum numbers.

Findings

Derived bound state energy eigenvalues and wave functions.

Analyzed special cases like Morse and generalized Morse potentials.

Explored non-relativistic limits of the solutions.

Abstract

Approximate analytic solutions of the Dirac equation with Tietz-Hua (TH) potential are obtained for arbitrary spin-orbit quantum number using the Pekeris approximation scheme to deal with the spin-orbit coupling terms In the presence of exact spin and pseudo-spin (pspin) symmetric limitation, the bound state energy eigenvalues and associated two-component wave functions of the Dirac particle moving in the field of attractive and repulsive TH potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The cases of the Morse potential, the generalized Morse potential and non-relativistic limits are studied.