Supervelocity in Tunneling?
Following Hartman (Journal of Applied Physics 33, 3427 (1962)), the transmission time tHa of an incident Gaussian wave packet through a symmetric rectangular barrier is usually taken as the difference between the time at which the peak of the transmitted packet leaves the barrier of thickness ℓ and the time at which the peak of the incident Gaussian wave packet arrives at the barrier. This yields a corresponding transmission velocity cHa = ℓ/tHa which appears under certain conditions as a supervelocity, i.e. becomes larger than the corresponding propagation velocity in free space which is the group velocity for electrons or the velocity of light for photons, respectively. However, as shown in this publication, the peak of an incident Gaussian wave packet and the peak of the transmitted wave packet are in no causal relationship. The shape of the transmitted wave packet is produced from the incident wave by convolution with the pulse response of the barrier. This yields a distortion of the shape of the wave packet which includes also the observed negative time shift of the peak.
Publications
Misinterpretation yields supervelocities during transmission of wave packets through a barrier
J. Weis, O. Weis
European Physical Journal B 12, 135 (1999)