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Annals of Physics

High-energy, semiclassical scattering processes

Bernard A. Lippmann

Published May 1, 1957• 17 citations
Publisher
DOI
10.1016/0003-4916(57)90054-4

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Semiclassical approximations for tunnelling processes usually involve complex trajectories or complex times. In this paper, we use a previously derived approximation involving only real trajectories propagating in real time to describe the scattering of a Gaussian wavepacket by a finite square potential barrier. We show that the approximation describes both tunnelling and interferences very accurately in the limit of small Planck’s constant. We use these results to estimate the tunnelling time of the wavepacket and find that, for high energies, the barrier slows down the wavepacket but that it speeds it up at energies comparable to the barrier height. PACS numbers: 03.65.Sq, 31.15.Gy (Some figures in this article are in colour only in the electronic version.) 1.
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