Simple way to extract solutions and features of the Dirac equation for a noncentral potentials

The main purpose of the present study is to explore the classes of the Schrödinger-like wave equations derived from Dirac equation, for which the similarity transformation and asymptotic iteration algorithms can assist in generating second-order differential equation that admit general exact solutions in the presence of nonsymmetrical potential terms. For illustration purposes, we extract the exact bound-state solutions of the Dirac equation with the noncentral Hartmann potential for the cases of exact [Formula: see text] spin and pseudospin symmetries. Also, we have shown that both Dirac-radial and Dirac-polar parts are sensitive to the variation of the involved parameters.

EXACT SOLUTIONS OF DIRAC EQUATION WITH HARTMANN POTENTIAL BY NIKIFOROV–UVAROV METHOD

We investigate the exact solution of the Dirac equation for the Hartmann potential. The radial and polar parts of the Dirac equation are solved by Nikiforov–Uvarov method. The bound state energy eigenvalues and the corresponding two-component spinor wave functions of the Dirac particles are obtained.

EXACT SOLUTION OF THE CONTINUOUS STATES FOR GENERALIZED ASYMMETRICAL HARTMANN POTENTIALS UNDER THE CONDITION OF PSEUDOSPIN SYMMETRY

Under the condition of pseudospin symmetry, the exact solution of Dirac equation is studied and that no bound solutions are observed for generalized asymmetrical Hartmann potential, which is in agreement with that for Coulomb potential. With the analytic continuation method, the unbound solutions are presented by mapping the wave functions of bound states in the complex momentum plane. Furthermore, the scattering phase shifts are obtained from the radial wave function by analyzing the asymptotic behavior of the confluent hypergeometric functions.