Quantum trajectories from kinematic considerations

Abstract

We present a method in which one can infer deterministic particle trajectories for quantum mechanics using just the time evolving probability density ρ = ψ*ψ and without assuming or solving any equations of motion. The approach utilizes the geometrical construction of centroidal Voronoi tessellations (CVT). In one dimension the CVT trajectories are shown to be identical to the particle trajectories of Bohm's quantum mechanics. Several two-dimensional numerical examples are given in which the resulting CVT trajectories are highly correlated with Bohm's trajectories. The method also allows the formation of trajectories for classical probability densities, for which the resulting trajectories are not, in general, the physically observed trajectories. Rather, they are hydrodynamic trajectories which kinematically depict the evolving density.