  In this work, a spin $\frac 12$ 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.
