Betz, Volker, Joye, Alain and Teufel, Stefan (2009) Emergence of exponentially small reflected waves. Asymptomatic Analysis, Vol.64 (No.1-2). pp. 53-100. doi:10.3233/ASY-2009-0935 ISSN 0921-7134.

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Asymptomatic Analysis
Publisher:	IOS Press
ISSN:	0921-7134
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.64
Number:	No.1-2
Number of Pages:	48
Page Range:	pp. 53-100
DOI:	10.3233/ASY-2009-0935
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/D07181X/1 (EPSRC)

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