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( 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.