Supersymmetric Patterns in the Pseudospin Spin and Coulomb Limits of the Dirac Equation with Scalar and Vector Potentials

Abstract

We show that the Dirac equation in 3+1 dimensions gives rise to supersymmetric patterns when the scalar and vector potentials are (i) Coulombic with arbitrary strengths or (ii) when their sum or difference is a constant, leading to relativistic pseudospin and spin symmetries. The conserved quantities and the common intertwining relation responsible for such patterns are discussed.