Relationship between dwell, transmission and reflection tunnelling times

Abstract

The transmission tunnelling time through a barrier is often defined as the probability that the particle is in the barrier divided by the transmission probability current density. The dwell time, the time the particle stays in the barrier, is commonly defined as the probability that the particle is in the barrier divided by the incident probability current density. We define the reflection tunnelling time in a similar way by dividing the probability that the particle is in the barrier by the reflection current density. By conservation of probability, the reciprocal of the dwell time is equal to the sum of the reciprocals of the transmission and reflection times. This relation is illustrated by calculating the different tunnelling times for a rectangular barrier.