Group theoretic approach for a Dirac particle in Coulomb-like potentials

The energy levels of the Dirac equation with a Kohn-Sham (KS) potential are obtained using algebraic perturbation theory based on the dynamical group structure SO(2,1) without making any non-relativistic approximation. It has been shown that this formalism reproduces the exact analytical result for the eigenvalues of the Dirac equation with both vector and scalar Coulomb potentials. The lowest-order results obtained from the analytical formulae are found to be in excellent agreement with exact numerical results.

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