Tunneling times for one-dimensional systems

We derive a general expression for the tunneling time in layered systems based on the Larmor-clock approach. We show that our results are equivalent to those obtained by the Feynman path-integral technique. We establish a relation between functional derivatives of the barrier potential and partial derivatives with respect to the incident energy. In application, we computed the tunneling time and the reflection time for a rectangular barrier, for a double rectangular barrier, and for a Gaussian potential.