Dirac Equation with vector and scalar potentials via Supersymmetry in Quantum Mechanics

Abstract

In this work, a spin $\frac{1}{2}$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators from supersymmetry in quantum mechanics. This formalism is applied for the generalized Dirac-Coulomb problem, which is an exactly solvable potential in relativistic quantum mechanics. We obtain the energy eigenvalues and calculate explicitly the energy eigenfunctions for the ground state and the first excited state.

14 pages, to be submitted to Phys. Lett. A

References in corpus (1)

• Supersymmetry in the Dirac equation for generalized Coulomb potential