Comment on “Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term” [J. Math. Phys. 51, 023525 (2010)]

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 is 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 2F1(a, b, c; z). The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.

Path integral solution for a Klein–Gordon particle in vector and scalar deformed radial Rosen–Morse-type potentials

“…The motion takes place in the half-space r > r 0 = 1 2α ln(−q). The figure 1 represents the variations with (αr) of the deformed Manning-Rosen potential (18) for three different |q| values. In order to construct the path integral for a state of orbital quantum number l, we first use the expression…”

“…In the case where q = 1, the potentials (1) reduce to the usual radial Rosen-Morse potential that has been investigated from different points of view in the last decade [5,6,7,8,9,10,11,12,13]. Also, for −1 ≤ q < 0 or q > 0, various methods have been used to solve the Klein-Gordon and Dirac equations [14,15,16,17,18] with these same potentials. In particular, for |q| = 1 and for a light modification of expression (1), the relativistic rotational-vibrational energies and the radial wave functions have been approximately calculated with the help of the supersymmetric WKB approach and through the resolution of the Klein-Gordon equation [19].…”

Complete solutions of the Dirac equation with q-deformed hyperbolic Pöschl-Teller potential plus a trigonometric Scarf II potential

“…Further, Meng et al [6] have proved that the pseudospin symmetry occurs for the more general condition dΣ(r)/dr = 0. Moreover, the solutions of the Dirac equation with spin and pseudospin symmetries have been obtained for many typical radial potentials such as the Morse potential [7][8][9], the Hulthén potential [10,11], the Rosen-Morse potential [12,13], the Manning-Rosen potential [14][15][16], the Pöschl-Teller potential [17], the second Pöschl-Teller like potential [18] and the generalized Woods-Saxon potential [19]. Recently, de Oliveira and Schmidt [20,21] have studied the Dirac equation for some potentials under the spin and pseudospin symmetries in curved spacetime.…”