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

Emergent Quantum Mechanics 2015

Tsai, Hung-Ming^1 ; Poirier, Bill^1

Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock

TX

79409-1061, United States^1

关键词: Interference effects;    Nonrelativistic quantum mechanics;    Probability densities;    Quantum wave packets;    Relativistic quantum mechanics;    Relativistic quantum theory;    Straight-line paths;    Wave packet propagation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/701/1/012013/pdf
DOI  :  10.1088/1742-6596/701/1/012013

来源: IOP

【 摘 要 】

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.