Manifestations the hidden symmetry of Coulomb problem in the relativistic quantum mechanics - from Pauli to Dirac electron

Tamari T. Khachidze, Anzor A. Khelashvili

Published 2005-07-27, updated 2005-07-28Version 2

The theorem known from Pauli equation about operators that anticommute with Dirac's $K$-operator is generalized to the Dirac equation. By means of this theorem the operator is constructed which governs the hidden symmetry in relativistic Coulomb problem (Dirac equation). It is proved that this operator coincides with the familiar Johnson-Lippmann one and is intimately connected to the famous Laplace-Runge-Lenz (LRL) vector. Our derivation is very simple and informative. It does not require a longtime and tedious calculations, as is offten underlined in most papers.