Bohm Trajectories and the Tunneling Time Problem

Abstract

Although many approaches based on conventional interpretations of quantum mechanics have been developed for calculating the average time taken for an electron to tunnel through a potential barrier, a satisfactory solution remains elusive. These approaches are discussed very briefly, focussing on the question of whether the concept of ‘tunneling time’ or, more generally, ‘mean transmission time’ is a meaningful one. Then it is shown that Bohm’s causal or trajectory interpretation provides a well-defined and unambiguous prescription for calculating transmission times that are conceptually meaningful within that interpretation. Results of such calculations are presented for single and double rectangular barriers. The time-modulated rectangular barrier is treated in detail to emphasize the importance of considering distributions of transmission and reflection times and not just the mean transmission time. Finally, the possibility of determining tunneling times experimentally is discussed.