Particle motion associated with wave-function density gradients

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.