Resonant tunneling with zero reflection at the classical velocity

Abstract

An important aspect of resonant tunneling with a probability of unity (thus zero reflection) through a finite region with length l is studied. The relation between the velocity expectation value $<\hat v_{res}>$ restricted to a region of length l and the tunneling time $\tau_{res}$ through the same region is calculated. The obtained result is the analogue of the mean velocity in classical mechanics: The velocity expectation value equals exactly the length divided by the tunneling time. This result holds for any potential but is especially relevant for finite periodic potentials and inversion symmetric potentials where resonances show a tunneling probability of unity.