Geodesic
Asymptotics of wave functions of the~stationary Schr\"odinger equation in the~Weyl chamber
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 269-278

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{TMF_2018_197_2_a5,
     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},
     pages = {269--278},
     publisher = {mathdoc},
     volume = {197},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a5/}
}
TY  - JOUR
AU  - S. Yu. Dobrokhotov
AU  - D. S. Minenkov
AU  - S. B. Shlosman
TI  - Asymptotics of wave functions of the~stationary Schr\"odinger equation in the~Weyl chamber
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 269
EP  - 278
VL  - 197
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a5/
LA  - ru
ID  - TMF_2018_197_2_a5
ER  - 
%0 Journal Article
%A S. Yu. Dobrokhotov
%A D. S. Minenkov
%A S. B. Shlosman
%T Asymptotics of wave functions of the~stationary Schr\"odinger equation in the~Weyl chamber
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 269-278
%V 197
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a5/
%G ru
%F TMF_2018_197_2_a5
S. Yu. Dobrokhotov; D. S. Minenkov; S. B. Shlosman. Asymptotics of wave functions of the~stationary Schr\"odinger 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/