The Dirac oscillator. A relativistic version of the Jaynes-Cummings model

The dynamics of wavepackets in a relativistic Dirac oscillator (DO) is comp ared with that of the Jaynes-Cummings model. The strong spin-orbit coupling of the DO produces the entanglement of the spin with the orbital motion si milar to that observed in the model of quantum optics. The resulting collap ses and revivals of the spin extend to a relativistic theory our previous f indings on a nonrelativistic oscillator where they were known as spin-orbit pendulum. The Foldy-Wouthuysen transformation can be performed exactly for the DO. It produces the well known smoothing effect over the Compton wavel ength. Thus, after this transformation, zitterbewegung disappears just as t he components of the WP associated to negative energy states.