On the connections between the classical and quantum-mechanical Kepler problems
Joachim Dahl, Thomas Godsk Jørgensen
The Runge-Lenz vector, which accounts for the accidental degeneracy of the non-relativistic Kepler problem, has been the subject matter of many studies, both in quantum mechanics and in classical mechanics. Much less attention has been paid to the Johnson-Lippmann operator which accounts for the accidental degeneracy of the relativistic Kepler problem in Dirac`s quantum-mechanical description. In the present communication we discuss the properties of the Johnson-Lippmann operator. We show its relation to the non-relativistic Runge-Lenz vector and draw a connection to Sommerfield`s early discussion of the relativistic Kepler problem. This enables us, inter alia, to give an explanation of the apparent coincidence of the energy expressions of the two theories.
Bulletin of the American Physical Society•May 1, 1993•0 citations