Exact solution of the Dirac equation for a Coulomb and scalar potential in the presence of an Aharonov–Bohm and a magnetic monopole fields

Abstract

In the present paper the problem of a relativistic Dirac electron is analyzed 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. The energy spectrum is computed and its dependence on the intensity of the Aharonov–Bohm and the magnetic monopole strengths is analyzed.