Bound states of (2+1)-dimensional massive Dirac fermions in a Lorentzian-shaped inhomogeneous perpendicular magnetic field

In this paper, we investigate massive Dirac fermions in (2 + 1)-spacetime confined by a Lorentzian-shaped inhomogeneous magnetic field and construct solutions of their bound states by both analytical and numerical methods. First, we have found a set of specific magnetic fields which allow obtaining conditionally exact solutions as well as quasi-exact ones. Second, we construct these analytical solutions explicitly and analyse the effect of Dirac fermion's effective mass. We also calculate entire energy spectra for the considered system numerically using Feranchuk-Komarov operator method and combine them with the analytical solutions for investigating Landau quantization in the energy spectrum.