Free Dirac wave packets with negative position-velocity covariance

Abstract

Building on the work of Robinett, et al. [Found. Phys. Lett. 18, 455 (2005)], we construct contractive solutions to the 1D free time-dependent Dirac equation (TDDE). We demonstrate that the position-velocity (xv) covariance is the physically appropriate measure for tracking a Dirac wave packet's contraction, as its vanishing time (τ_xv) coincides exactly with the contraction time (τ). Furthermore, we highlight two distinctly relativistic effects: contractive Dirac wave packets initially Gaussian in momentum space lose their Gaussian spatial profile, and their contraction time depends on the initial mean momentum, a feature completely absent in the nonrelativistic regime.