Calculation of the tunneling time using the extended probability of the quantum histories approach

The dwell time of quantum tunneling has been derived by Steinberg (1995) [7] as a function of the relation between transmission and reflection times τt and τr, weighted by the transmissivity and the reflectivity. In this paper, we reexamine the dwell time using the extended probability approach. The dwell time is calculated as the weighted average of three mutually exclusive events. We consider also the scattering process due to a resonance potential in the long-time limit. The results show that the dwell time can be expressed as the weighted sum of transmission, reflection and internal probabilities.