Geodesic
Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 269-278
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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 $U(\mathbf x)=\sum_{j=1}^nV(x_j)$, ${\mathbf x=(x_1,\dots,x_n)\in\mathbb R^n}$, 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, Maslov canonical operator, Airy function.
Mots-clés : quantization condition 
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     author = {S. Yu. Dobrokhotov and D. S. Minenkov and S. B. Shlosman},
     title = {Asymptotics of wave functions of the~stationary {Schr\"odinger} equation in {the~Weyl} chamber},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a5/}
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S. Yu. Dobrokhotov; D. S. Minenkov; S. B. Shlosman. Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 269-278. http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a5/

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