Relativistic extension of shape-invariant potentials

Abstract

The Dirac equation for a charged spinor in an electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape-invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Mörse I and II, Eckart, Pöschl-Teller and Scarf potentials.