Particle motion associated with wave function density gradients

TL;DR

This paper investigates how quantum wave function density gradients influence particle velocities in coupled waveguides, revealing energy-velocity relationships and effects of gain/loss regions on particle speed.

Contribution

It introduces a novel scheme linking population transfer in coupled waveguides to particle velocity measurement and explores the roles of phase and density gradients in quantum motion.

Findings

Velocity relates to energy in forbidden regions.

Gain and loss regions accelerate particles.

Phase and density gradients indicate particle speed.

Abstract

We study the quantum mechanical motion of massive particles in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock and allows particle velocities to be determined. Application of this scheme to evanescent phenomena at a reflective step potential reveals an energy-velocity relationship for classically forbidden motion. Regions of gain and loss, as described by imaginary potentials, are shown to speed up the motion of particles. We argue that phase and density gradients in quantum mechanical wave functions play complementary roles in indicating the speed of particles.