Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamberстатья
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Дата последнего поиска статьи во внешних источниках: 9 января 2019 г.
Аннотация: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(x)=∑j=1nV(xj),x=(x1,…,xn)∈ℝn, 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 xj. We propose a method for implementing the Maslov canonical operator in the form of the Airy function based on canonical transformations.