Space-time evolution of Dirac wave packets

TL;DR

This paper investigates the evolution of 3D relativistic Gaussian wave packets with various spin polarizations, analyzing their dynamics, symmetries, and transient behaviors to aid future experimental interpretations.

Contribution

It provides analytical and numerical solutions for Dirac wave packets with different symmetries, linking initial state symmetry to dynamical properties and Zitterbewegung parameters.

Findings

Analytical and numerical solutions for Dirac wave packets with various symmetries.

Calculated average velocity and spin of wave packets.

Identified parameters of transient Zitterbewegung in different directions.

Abstract

In this work we study the dynamics of free 3D relativistic Gaussian wave packets with different spin polarization. We analyze the connection between the symmetry of initial state and the dynamical characteristics of moving particle. The corresponding solutions of Dirac equation having different types of symmetry were evaluated analytically and numerically and after that the electron probability densities, as well as, the spin densities were visualized. The average values of velocity of the packet center and the average spin were calculated analytically, and the parameters of transient Zitterbewegung in different directions were obtained. These results can be useful for the interpretation of future experiments with trapped ions.