ua nt - p h / 99 12 10 9 v 1 2 6 D ec 1 99 9 Time of Arrival Through Interacting Environments — tunnelling case —

We discuss the propagation of wave packets through interacting environments. Such environments generally modify the dispersion relation or shape of the wave function. To study such effects in detail, we define the distribution function PX(T ), which describes the arrival time T of a packet at a detector located at point X. We calculate PX(T ) for wave packets travelling through a tunnelling barrier and find that our results actually explain recent experiments. We compare our results with the Nelson’s stochastic interpretation of quantum mechanics and resolve a paradox previously given by the Nelson’s viewpoint about the tunnelling time.