Bohmian transmission and reflection dwell times without trajectory sampling

Abstract

Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here a trajectory free formulation for the average transmission and reflection dwell times within static spatial intervals [a,b] is given for one-dimensional scattering problems. This formulation reduces the computation time to less than 5% of the computation time by means of trajectory sampling.

14 pages, 7 figures; v2: published version, significantly revised and shortened (former sections 2 and 3 omitted, appendix A added, simplified mathematics)