Solution of the Dirac equation with magnetic monopole and pseudoscalar potentials

The Dirac equation in the presence of the Dirac magnetic monopole potential, the Aharonov-Bohm potential, a Coulomb potential and a pseudo-scalar potential, is solved by separation of variables using the spinweighted spherical harmonics. The energy spectrum and the form of the spinor functions are obtained. It is shown that the number j in spin-weighted spherical harmonics must be greater than $\left| q \right| - \tfrac{1} {2}$ .