Algebraic derivation of spectrum of the Dirac Hamiltonian for arbitrary combination of Lorentz-scalar and Lorentz-vector Coulomb potentials

TL;DR

This paper derives the spectrum of the Dirac Hamiltonian with mixed Lorentz-scalar and Lorentz-vector Coulomb potentials algebraically, confirming known solutions through a superalgebra approach.

Contribution

It introduces an algebraic derivation method for the Dirac spectrum with combined potentials, extending prior explicit solutions.

Findings

Spectrum matches known explicit solutions

Algebraic method confirms previous results

Applicable to arbitrary potential combinations

Abstract

Spectrum of the Dirac Equation is obtained algebraically for arbitrary combination of Lorentz-scalar and Lorentz-vector Coulomb potentials using the Witten's Superalgebra approach. The result coincides with that, known from the explicit solution of Dirac equation.