Spin-orbit pendulum - Relativistic extension

Abstract

We discuss an extension of the theory of {\em spin-orbit pendulum} phenomenon given in [1] to relativistic approach. It is done within the so called Dirac Oscillator. Our first results, focusing on circular wave packet motion have been published recently [2]. The scope of this paper is motion of a linear wave packet. In relativistic approach we found {\em Zitterbewegung} in spin-orbit motion (in Dirac representation) due to coupling to negative energy states. This effect is washed out in the Foldy-Wouthuysen representation. Another important change with respect to non-relativistic case is the loss of periodicity. The phenomenon reminds the time evolution of population inversion in Jaynes-Cummings model.

4 pages, LaTeX2e (appolb.cls included). Presented at XXVI Mazurian Lakes School of Physics on Nuclear Physics at the Turn of the Century, Krzyze, Poland, September 1-11, 1999. To appear in Acta Phys. Polon. B (2000)