  In the present article we analyze the problem of a relativistic Dirac
electron in the presence of a combination of a Coulomb field, a $1/r$ scalar
potential as well as a Dirac magnetic monopole and an Aharonov-Bohm potential.
Using the algebraic method of separation of variables, the Dirac equation
expressed in the local rotating diagonal gauge is completely separated in
spherical coordinates, and exact solutions are obtained. We compute the energy
spectrum and analyze how it depends on the intensity of the Aharonov-Bohm and
the magnetic monopole strengths.
