Traversal Time for Tunneling

One of several contradictory existing results for the time a tunneling particle interacts with its barrier is confirmed, by considering tunneling through a time-modulated barrier. At low modulation frequencies the traversing particle sees a static barrier. At high frequencies the particle tunnels through the time-averaged potential, but can do it inelastically, losing or gaining modulation quanta. The transition between the two regimes yields $\int \mathrm{dx}{\left[\frac{m}{2(V-E)\mathrm{}}\right]}^{\frac{1}{2}}$ for the traversal time.