Algebraic approach to quasi-exact solutions of the Dirac-Coulomb problem

The Dirac equation in the presence of Coulomb electrostatic potential is solved and the quasi-exact solutions are obtained via osp(2, 2) algebraization. The Lie-algebraic approach of quasi-exact solvability is applied to the problem and by constructing the matrix representation of the problem, the energy spectrum and thereby the corresponding spinor wave functions are obtained in terms of the polynomial components of osp(2, 2) superalgebra.