Which is the right way to calculate the tunneling time?
The tunneling time is a topic of ongoing experimental interest (1), and there is no agreement about its theoretical definition. The determination of the tunneling time of a wavepacket through a barriere with the stationary phase method predicts a fixed value for the tunneling time that is independent of the thickness of the barriere (Hartmann effect, (2)). We have solved the problem of wavepacket tunneling with the method of Laplace transform (3) which gives an explicit picture of the transmission/reflection process. We found that there is not one single reflection/transmission, but that subsequent wave packages leave the barriere at both sides. We also found a fixed tunneling time that coincides with the time found by Hartmann. This result makes sure that the Hartman time is not an artefact of the stationary phase method. It seems to be a characteristic and fundamental parameter of the tunneling process and it should be possible to verify its distinct value experimentally.
(1) A.Fortun et al. (2016): Direct Tunneling Delay Time Measurement in an Optical Lattice, Phys.Rev.Lett 16/117(1)/010401
A.S.Landsmann et. al (2014): Ulreafast resolution of tunneling delay time, Optica 1/5/343-349
(2) T. Hartmann(1962):Tunneling of a Wave packet, J.Appl. Phys. 33, 3427
(3) N. Riahi(2017): Solving the time-dependent Schrödinger equation via Laplace transform, Quantum Stud.: Math. Found 4/2,103-126