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Physics Essays

A Model for Relativistic Motion and Spin

Joseph Shaffer

Published Mar 1, 1994• 2 citations
Publisher
DOI
10.4006/1.3029113

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We discuss an extension of the theory of 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 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. PACS numbers: 03.65.Sq, 03.65.Ge 1.
The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a relativistic theory our previous findings on nonrelativistic oscillator where they were known under the name of `spin-orbit pendulum'. There are important relativistic effects (lack of periodicity, zitterbewegung, negative energy states). Many of them disappear after a Foldy-Wouthuysen transformation.