Quantum mechanical Gaussian wavepackets of single relativistic particles
arXiv:2309.09429 · doi:10.1016/j.cjph.2023.11.017 10.1016/j.cjph.2026.09.023
Abstract
We study the evolutions of selected quasi-(1+1) dimensional wavepacket solutions to the Klein-Gordon equation for a relativistic charged particle in uniform motion or accelerated by a uniform electric field in Minkowski space. We explore how good the charge density of a Klein-Gordon wavepacket can be approximately described by a Gaussian state with the single-particle interpretation. We find that the minimal initial width of a wavepacket for a good Gaussian approximation in position space is about the Compton wavelength of the particle divided by its Lorentz factor at the initial moment. This can be considered as a manifestation of relativistic length contraction, which is also observed numerically in the spreading of the wavepacket's charge density.
arXiv comment17 pages, 8 figures. v2: Ref.[6] has been added. v3: Eq.(24) has been corrected, and Figs. 6 and 7 have been revised accordingly. The observation and conclusion remain unchanged
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