Supersymmetry in the Dirac equation for generalized Coulomb potential

Details Supersymmetry in the Dirac equation for generalized Coulomb potential Supersymmetry in the Dirac equation for generalized Coulomb potential

2007-01-29

arxiv.org/abs/hep-th/0701259v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages. Submitted to Phys. Rev. A

Scientific paper

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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