Supersymmetry and the Dirac Equation with Vector and Scalar Coupling Potentials

This paper shows that one type of first order Dirac equation with vector coupling and scalar coupling potentials can be brought into the framework of non relativistic supersymmetric quantum mechanics. The conclusion is independent of the concrete forms of the vector and scalar coupling potentials because of the nilpotent matrix realization of supersymmetric quantum mechanical algebra. The supersymmetry of this kind of Dirac equation requires that a spin orbit coupling term be introduced into the associated supersymmetric Hamiltonian.