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TMF, 2018, Volume 197, Number 2, Pages 269–278 (Mi tmf9552)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber

S. Yu. Dobrokhotovab, D. S. Minenkova, S. B. Shlosmancde

a Ishlinsky Institute for Problems of Mechanics, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia
c Skolkovo Institute of Science and Technology, Москва, Россия
d Aix Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France
e Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

Abstract: We study stationary solutions of the Schrödinger equation with a monotonic potential $U$ in a polyhedral angle (Weyl chamber) with the Dirichlet boundary condition. The potential has the form $U(\mathbf x)=\sum_{j=1}^nV(x_j)$, ${\mathbf x=(x_1,…,x_n)\in\mathbb R^n}$, with a monotonically increasing function $V(y)$. We construct semiclassical asymptotic formulas for eigenvalues and eigenfunctions in the form of the Slater determinant composed of Airy functions with arguments depending nonlinearly on $x_j$. We propose a method for implementing the Maslov canonical operator in the form of the Airy function based on canonical transformations.

Keywords: stationary Schrödinger equation, boundary value problem, Weyl-chamber-type polyhedral angle, spectrum, quantization condition, Maslov canonical operator, Airy function.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-51-150006
This research is supported by the Russian Foundation for Basic Research–CNRS (Grant No. 17-51-150006).


DOI: https://doi.org/10.4213/tmf9552

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English version:
Theoretical and Mathematical Physics, 2018, 197:2, 1626–1634

Bibliographic databases:

Document Type: Article
PACS: 03
MSC: 34E20, 34B05
Received: 16.02.2018

Citation: S. Yu. Dobrokhotov, D. S. Minenkov, S. B. Shlosman, “Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber”, TMF, 197:2 (2018), 269–278; Theoret. and Math. Phys., 197:2 (2018), 1626–1634

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dobrokhotov S.Yu., Nazaikinskii V.E., “Efficient Formulas For the Maslov Canonical Operator Near a Simple Caustic”, Russ. J. Math. Phys., 25:4 (2018), 545–552  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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