ИСТИНА

The Schrodinger equation with a monotonic potential U in a polyhedral angle (Weyl chamber) with the Dirichlet boundary condition is studied. The potential has the form U(x1,...,xn) = V(x1) + ... + V(xn), V′(x) > 0. Semiclassical asymptotic formulas for eigenfunctions can be constructed using the Slater determinant composed of Airy functions with arguments depending nonlinearly on x. Eigen-values are found from corresponding quantization conditions. Such asymptotics are valid uniformly for small and large wave numbers. These results are obtained together with S.Yu. Dobrokhotov and S.B. Shlosman and are supported by the Russian Foundation for Basic ResearchCNRS (Grant No. 17-51-150006).