Abstract : 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.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00462988
Contributor : Ludovic Jaubert
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Submitted on : Monday, March 22, 2010 - 4:33:12 PM
Last modification on : Thursday, April 19, 2018 - 2:54:03 PM
Long-term archiving on : Tuesday, September 28, 2010 - 11:41:24 AM
Ludovic Jaubert, Marcus de Aguiar. Semiclassical tunnelling of wavepackets with real trajectories. Physica Scripta, IOP Publishing, 2007, 75 (3), pp.363-373. ⟨10.1088/0031-8949/75/3/023⟩. ⟨ensl-00462988⟩
