Emergence of exponentially small reflected waves

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dc.creatorBetz, Volker
dc.creatorJoye, Alain
dc.creatorTeufel, Stefan
dc.date2008-04-23
dc.date.accessioned2026-07-07T09:34:17Z
dc.date.available2026-07-07T09:34:17Z
dc.descriptionWe 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.
dc.description44 pages
dc.identifierhttps://arxiv.org/abs/0804.3717
dc.identifierhttp://arxiv.org/abs/0804.3717
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159441
dc.subjectMathematical Physics
dc.subject41A60; 81Q05
dc.titleEmergence of exponentially small reflected waves
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