Asymptotics of Wave Functions of the Stationary Schrodinger Equation in the Weyl Chamber

We study stationary solutions of the Schrodinger equation with a monotonic potential U in a polyhedral angle (Weyl chamber) with the Dirichlet boundary condition. The potential has the form U(x)=Sigma j=1(n) V(x(j)), x = (x(1),...,x(n)) is an element of 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.