Discrete spectra of the Dirac Hamiltonian in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions

We find all self-adjoint Dirac Hamiltonians in Coulomb and Aharonov–Bohm potentials in $2+1$ dimensions with the fermion spin taken into account. We obtain implicit equations for the spectra and construct eigenfunctions for all self-adjoint Dirac Hamiltonians in the indicated external fields. We find explicit solutions of the equations for the spectra in some cases.