Quasi-exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Abstract

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra $sl(2)$ which underlies most one-dimensional and effectively one-dimensional quasi-exactly solvable systems. In this paper we demonstrate that the quasi-exactly solvable differential equation possesses a hidden $osp(2,2)$ superalgebra.