Dirac equation for the harmonic scalar and vector potentials and linear plus coulomb-like tensor potential; the SUSY approach

Abstract

The problem of analytical solutions of the 3-dimensional Dirac equation is usually studied via techniques such as The Nikiforov–Uvarov (NU) method. Here, we see that one of the most attractive potentials can be brought into a well-known form of Schrödinger-like problem possessing known solutions via the methodology of supersymmetry (SUSY). Next, using the idea of shape invariance, we calculate exact solutions of Dirac equation for quadratic scalar and vector potentials in the presence of a tensor potential that depends on the radial component either linearly or inversely. The tensor potential itself, besides its applications, removes degeneracy, too.