Comment on "Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term"

TL;DR

This paper critiques a previous application of the Nikiforov-Uvarov method to the Dirac equation with the Rosen-Morse potential, showing it yields incorrect energy spectra and unphysical wave functions, and clarifies the correct solution form.

Contribution

It demonstrates the inadequacy of the previous method and provides the correct form of the wave functions and energy eigenvalues involving hypergeometric functions.

Findings

Previous solutions are incorrect and physically unacceptable.

Correct wave functions involve generalized hypergeometric functions.

Bound state energies are determined by a transcendental equation.

Abstract

It is shown that the application of the Nikiforov-Uvarov method by Ikhdair for solving the Dirac equation with the radial Rosen-Morse potential plus the spin-orbit centrifugal term is inadequate because the required conditions are not satisfied. The energy spectra given are incorrect and the wave functions are not physically acceptable. We clarify the problem and prove that the spinor wave functions are expressed in terms of the generalized hypergeometric functions. The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.