  Exact solutions are found to the Dirac equation for a combination of Lorentz
scalar and vector Coulombic potentials with additional non-Coulombic parts. An
appropriate linear combination of Lorentz scalar and vector non-Coulombic
potentials, with the scalar part dominating, can be chosen to give exact
analytic Dirac wave functions. The method works for the ground state or for the
lowest orbital state with l=j-{1/2}, for any j.
