Supersymmetric patterns in the pseudospin, spin, and coulomb limits of the dirac equation with scalar and vector potentials

A common interwining relation providing a basis for a unified treatment of three seperate limits at which a Dirac Hamiltonian, with scalar and vector potentials exhibited supersymmetric patterns was discussed. It was shown that in the Coulomb limit, the potentials were 1/r but their strength were otherwise arbitrary. In the pseudospin or spin limits, there were no restrictions on the r dependence of the potentials but a constraint on their sum or differences was there. It was observed that the characteristic degeneracies reflected the presence of additional conserved operators, Johnson-Lippman operator and the relativistic pseudospin and spin generators.