Tunneling times for opaque barriers

We propose new criteria to evaluate the average time spent by particles in a tunneling barrier. First we construct asojourn time, on the basis of statistical information provided by quantum mechanics, which seems to be an appropriate measure of the time spent byall particles within the barrier. A simple, stochastic treatment is then used to deal with the particles that actually traverse the barrier, in order to study their interaction time. The results obtained show that opaque barriers have important effects on the particlesbefore they enter the potential region, confirming previously published numerical findings. No arbitrarily high effective velocities appear anywhere in the present treatment.