Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

Hung Ming Tsai, Bill Poirier

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature - suggesting a "many interacting worlds" interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time - in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.

Original languageEnglish
Article number012013
JournalJournal of Physics: Conference Series
Issue number1
StatePublished - Mar 30 2016
Event3rd International Symposium on Emergent Quantum Mechanics, EmQM 2015 - Vienna, Austria
Duration: Oct 23 2015Oct 25 2015


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