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

Abstract. In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr¨odinger 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,