S. Panchanan et al., GROUP THEORETIC APPROACH FOR A DIRAC PARTICLE IN COULOMB-LIKE POTENTIALS, Journal of physics. A, mathematical and general, 28(22), 1995, pp. 6467-6477
The energy levels of the Dirac equation with a Kohn-Sham (KS) potentia
l are obtained using algebraic perturbation theory based on the dynami
cal group structure SO(2, 1) without making any non-relativistic appro
ximation. It has been shown that this formalism reproduces the exact a
nalytical result for the eigenvalues of the Dirac equation with both v
ector and scalar Coulomb potentials. The lowest-order results obtained
from the analytical formulae are found to be in excellent agreement w
ith exact numerical results.