An "Accidental" Symmetry Operator for the Dirac Equation in the Coulomb Potential

Abstract

On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is intimately connected to the familiar Laplace-Runge-Lenz vector. Our approach guarantees not only derivation of Johnson-Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian follows.

arXiv comment6 pages

References in corpus (1)

• Exact supersymmetry in the nonrelativistic hydrogen atom

Cited by in corpus (2)

• Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space
• Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron