Tunnelling times: An elementary introduction

In this paper we examine critically and in detail some existing definitions for the tunnelling times, namely: the phase-time; the centroid-based times; the Buttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time, and finally the generalized (Olkhovsky and Recami) dwell time, by adding also some numerical evaluations. Then, we pass to examine the equivalence between quantum tunnelling and photon tunnelling (evanescent waves propagation), with particular attention to tunnelling with Superluminal group-velocities (Hartman effect). At last, in an Appendix, we add a bird-eye view of all the experimental sectors of physics in which Superluminal motions seem to appear.