Emergence of exponentially small reflected waves

We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially small scattered part of the wave packet in the semiclassical...

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Bibliographic Details
Published in:arXiv.org 2008-04
Main Authors: Betz, Volker, Joye, Alain, Teufel, Stefan
Format: Article
Language:English
Subjects:
Flux density
Incident waves
Quantum mechanics
Reflected waves
Time dependence
Online Access:Get full text
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Summary:We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially small scattered part of the wave packet in the semiclassical parameter when the energy density of the incident wave is sharply peaked around some value. We prove that this reflected part has, to leading order, a Gaussian shape centered on the classical trajectory for all times soon after its birth time. We give explicit formulas and rigorous error bounds for the reflected wave for all of these times.
ISSN:2331-8422