Variational approach to the tunneling-time problem

Abstract

Tunneling problems are characterized by different quantum time scales of motion. In this paper, we identify a tunneling time scale, which is based on a simple variational principle. The method utilizes the stationary eigenfunctions for a given one-dimensional potential structure, and it provides a truly local definition of the tunneling time, independent of the asymptotic shape of the potential. We express the minimum tunneling time in terms of the more common time scales obtained from the Larmor clock setup. Asymptotic formulas for both the extreme quantum and the semiclassical limit are presented. As an experimental verification of the variational approach we demonstrate that the minimum tunneling time governs the time a particle requires to traverse the barrier in a symmetric double-well structure.