MORE ABOUT TUNNELING TIMES, THE DWELL TIME AND THE HARTMAN EFFECT

In a recent review paper [Phys. Reports 214 (1992) 339] we proposed, w ithin conventional quantum mechanics, new definitions for the sub-barr ier tunnelling and reflection times. Aims of the present paper are: i) presenting and analysing the results of various numerical calculation s (based on our equations) on the penetration and return times < tau(P en) >, < tau(Ret) >, during tunnelling inside a rectangular potential barrier, for various penetration depths x(f); ii) putting forth and di scussing suitable definitions, besides of the mean values, also of the variances (or dispersions) D tau(T). and D tau(R) for the time durati ons of transmission and reflection processes; nl) mentioning, moreover , that our definition < tau(T) > for the average transmission time res ults to constitute an improvement of the ordinary dwell-time tau(DW) f ormula: iv) commenting, at last, on the basis of our new numerical res ults, upon some recent criticism by C.R. Leavens. We stress that our n umerical evaluations confirm that our approach implied, and implies, t he existence of the Hartman effect: an effect that in these days (due to the theoretical connections between tunnelling and evanescent-wave propagation) is receiving - at Cologne, Berkeley, Florence and Vienna - indirect, but quite interesting, experimental verifications. Eventul ly, we briefly analyze some other definitions of tunnelling times.