Closed form perturbative relativistic modifications to wave-packet dynamics in the quantum harmonic oscillator
arXiv:2603.07954
Abstract
We derive closed form expressions of weak relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to wave-packet parameters, such as the time-dependent widths, variances, and uncertainty relations. Specific calculations are performed for unsqueezed, minimum-uncertainty Gaussian wave packets, valid up to leading order in (). When applied to electron wave packets, the results indicate that relativistic effects become non-negligible for keV-scale harmonic confinement energies: the deviations in variances reach for an electron wave packet confined within the energy range. We also show that the standard saturation of the uncertainty relation remains unaffected by the leading-order relativistic effect.
21 pages, no figures