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Wavepacket electron scattering

Laurence D. Marks

Published Jan 1, 1986• 0 citations
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Wavepacket theory of the Kapitza-Dirac effect

Maxim A. Efremov, Mikhail Vladimirovich Fedorov

The Kapitza-Dirac effect (KDE), or the scattering of electrons by a standing light wave, is considered quantum mechanically with electron states before scattering taken in the form of wavepackets with homogeneously distributed `centres of mass'. The angular distribution functions of electrons after scattering and the average angle of scattering are found. This approach is used to establish the applicability conditions of purely classical, purely quantum-mechanical and intermediate results in the theory of KDE, as well as to describe some new regimes of scattering, characteristics of which depend explicitly on the size of the wavepackets before scattering.

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Semiclassical tunnelling of wavepackets with real trajectories

Ludovic D. C. Jaubert, Marcus A. M. de Aguiar

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.

•Jan 1, 2007•5 citations
The Kapitza-Dirac effect (KDE), or the scattering of electrons by a standing light wave, is considered quantum mechanically with electron states before scattering taken in the form of wavepackets with homogeneously distributed `centres of mass'. The angular distribution functions of electrons after scattering and the average angle of scattering are found. This approach is used to establish the applicability conditions of purely classical, purely quantum-mechanical and intermediate results in the theory of KDE, as well as to describe some new regimes of scattering, characteristics of which depend explicitly on the size of the wavepackets before scattering.
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.