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arXiv:2603.07954 · Journal of Physics A Mathematical and Theoretical

Perturbative relativistic modifications to wave-packet dynamics and uncertainty relations in the quantum harmonic oscillator

Jian Carlo Ramos, Sujoy K. Modak

quant-phhep-thSubmitted Mar 9, 2026• Announced Mar 10, 2026• 0 citations
v1 · Mar 9, 2026v2 · May 28, 2026
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Abstract

We analyze 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 the wave-packet parameters such as the average position, width and the uncertainty relations. For Gaussian wave packets, these corrections admit closed-form analytic expressions at order $1/c^{2}$. When applied to electron wave packets, the results indicate that relativistic effects become non-negligible in the keV scale harmonic confinement energies -- the uncertainty relationship deviation reaches 0.1% to 1% for an electron wave-packet moving at 15% speed of light and confined within 1-10 keV energy range which might be experimentally verifiable.

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