Supersymmetry in the Dirac equation for generalized Coulomb potential

2007/01/29 by Tamar T. Khachidze, Khachidze, Tamar T., Anzor Khelashvili +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.hep-th/0701259

openalex publication_date 2007/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a symmetry of the Dirac equation under the interchange of signs of eigenvalues of the Dirac's K operator. We show that the only potential which obeys this requirement is the Coulomb one for both vector and scalar cases. 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 results coincides with that, known from the explicit solution of the Dirac equation.

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• Dirac Equation with vector and scalar potentials via Supersymmetry in Quantum Mechanics

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