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This article is cited in 6 scientific papers (total in 6 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
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.
Received: December 2, 2019 Revised: December 2, 2019 Accepted: May 16, 2020
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
Linking options:
https://www.mathnet.ru/eng/tm4103https://doi.org/10.4213/tm4103 https://www.mathnet.ru/eng/tm/v310/p322
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