Vortex-Enhanced Zitterbewegung in Relativistic Electron Wave Packets

TL;DR

This paper demonstrates that adding orbital angular momentum to relativistic electron wave packets significantly amplifies Zitterbewegung, potentially enabling its experimental observation in structured electron states.

Contribution

It introduces a relativistic vortex electron wave packet model that enhances Zitterbewegung amplitude, unifying Gaussian and Bessel-Gaussian states.

Findings

Orbital angular momentum amplifies ZBW amplitude.

Vortex states unify Gaussian and Bessel-Gaussian models.

Potential for observing relativistic quantum dynamics.

Abstract

Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent superposition of both positive- and negative-energy Dirac states and derive their space-time dynamics. Our analysis demonstrates that introducing orbital angular momentum provides a mechanism for amplifying the ZBW amplitude far beyond that of conventional Gaussian packets, while maintaining coherence. The resulting relativistic vortex states unify Gaussian and Bessel-Gaussian models within a single framework and opens new possibilities for observing relativistic quantum dynamics in structured electron wave packets.