Tunneling time through a rectangular barrier

Abstract

In this paper, we discuss the tunneling time of a quantum particle through a rectangular barrier. The reflection and transmission times associated with the wave packets representing the particle are discussed. By using an initial Gaussian momentum distribution, we carry out a comparative analysis of the stationary phases of the incident, reflected, and transmitted wave packets leading to the reflection and transmission times Dt R and Dt T , respectively. In the present treatment of this old and very known problem we take into account the deformations of the reflected and transmitted momentum distributions. These deformations produce a dependence of the reflection and transmission times on the location of the initial wave packet. In a parallel calculation, by numerically monitoring the time evolution of the system, we characterize a reflection and a transmission time. Such times agree with the ones obtained via the stationary phase method. @S1050-2947~98!07912-8# In the literature, we can find a number of papers suggesting different expressions for the so-called tunneling time, the time a quantum particle spends in a classically forbidden potential region. In particular, we cite some of those works that propose a method of associating the tunneling time with a phase time Dt w @1‐6#. According to such a method, the tunneling time is obtained from an analysis of the phase of the function that describes a wave packet incident on the potential.