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

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.