https://doi.org/10.1007/s100510050988
Misinterpretation yields supervelocities during transmission of wave packets through a barrier
1
Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569
Stuttgart, Germany
2
Fakultät für Naturwissenschaften, Universität Ulm, 89069 Ulm, Germany
Corresponding author: a weis@klizix.mpi-stuttgart.mpg.de
Received:
7
January
1999
Revised:
22
April
1999
Published online: 15 November 1999
This paper is concerned with the transmission time of an incident Gaussian
wave packet through a symmetric rectangular barrier. Following Hartman (J. Appl. Phys. 33, 3427 (1962)), the
transmission time is usually taken as the difference between the time
at which the peak of the transmitted packet leaves the barrier of thickness
and
the time at which the peak of the incident Gaussian wave packet arrives at the
barrier. This yields a corresponding transmission velocity
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. By analysing the propagation of a broadband wave packet (which leads
in free space to an extremely concentrated wave packet at a certain time)
we obtain the pulse response function of the barrier and show that
the insertion of the barrier is physically unable to produce a supervelocity.
Therefore, 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.
We demonstrate further that the phenomenon of Hartman's supervelocities is
not restricted to barriers with their exponentially decaying fields but occurs
for instance also in transmission lines with an inserted LCR circuit.
PACS: 73.40.Gk – Tunneling / 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aharonov Bohm effect, Bell inequalities, Berry's phase) / 05.60.Gg – Quantum transport
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999