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.
Abstract:We present a rigorous path integral treatment of a dynamical system in the axially symmetric potentialIt is shown that the Green's function can be calculated in spherical coordinate system for V (θ) = . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number ≥ 0, are recovered.
A hyperbolic-type potential with a centrifugal term is solved approximately using the path integral approach. The radial Green's function is expressed in closed form, from which the energy spectrum and the suitably normalized wave functions of bound and scattering states are extracted for (1/2) − [Formula: see text] < σ < (1/2) + [Formula: see text]. Besides, the phase shift and the scattering function Sl for each angular momentum l are deduced. The particular cases corresponding to the s-waves (l = 0) and the barrier potential (σ = 1) are also analyzed.
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