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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 310, Pages 322–331
DOI: https://doi.org/10.4213/tm4103 (Mi tm4103) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Semiclassical Asymptotics of the Solution to the Cauchy Problem for the Schrödinger Equation with a Delta Potential Localized on a Codimension 1 Surface

A. I. Shafarevichabcd, O. A. Shchegortsovae

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526 Russia
c National Research Center “Kurchatov Institute”, pl. Akad. Kurchatova 1, Moscow, 123182 Russia
d Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia
e Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
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DOI: https://doi.org/10.4213/tm4103
Abstract: We describe the semiclassical asymptotics of the solution to the Cauchy problem for the Schrödinger equation with a delta potential localized on a codimension $1$ surface. The initial condition represents a rapidly oscillating wave packet. We show that the asymptotics is expressed in terms of the Maslov canonical operator on a pair of Lagrangian manifolds in the extended phase space; the form of the delta potential defines a mapping between these manifolds that describes the reflection and scattering of the wave packet.
Funding agency Grant number
Russian Science Foundation 16-11-10069
This work is supported by the Russian Science Foundation under grant 16-11-10069.
Received: December 2, 2019
Revised: December 2, 2019
Accepted: May 16, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 310, Pages 304–313
DOI: https://doi.org/10.1134/S0081543820050223
Bibliographic databases:
Document Type: Article
UDC: 517.95+514.76
Language: Russian
Citation: A. I. Shafarevich, O. A. Shchegortsova, “Semiclassical Asymptotics of the Solution to the Cauchy Problem for the Schrödinger Equation with a Delta Potential Localized on a Codimension 1 Surface”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 322–331; Proc. Steklov Inst. Math., 310 (2020), 304–313
Citation in format AMSBIB
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\paper Semiclassical Asymptotics of the Solution to the Cauchy Problem for the Schr\"odinger Equation with a Delta Potential Localized on a Codimension 1 Surface
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 310
\pages 322--331
\publ Steklov Math. Inst.
\publaddr Moscow
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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