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

摘要

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.