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

• ##### Anzor A. Khelashvili
Modern Physics Letters A (Impact Factor: 1.11). 07/2005; DOI: 10.1142/S0217732305018505
Source: arXiv

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. Comment: 6 pages

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##### Article: Exact supersymmetry in the relativistic hydrogen atom in general dimensions -- supercharge and the generalized Johnson-Lippmann operator
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ABSTRACT: A Dirac particle in general dimensions moving in a 1/r potential is shown to have an exact N = 2 supersymmetry, for which the two supercharge operators are obtained in terms of (a D-dimensional generalization of) the Johnson-Lippmann operator, an extension of the Runge-Lenz-Pauli vector that relativistically incorporates spin degrees of freedom. So the extra symmetry (S(2))in the quantum Kepler problem, which determines the degeneracy of the levels, is so robust as to accommodate the relativistic case in arbitrary dimensions.
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