SEMICLASSICAL ASYMPTOTICS OF THE SPECTRUM OF THE HYDROGEN ATOM IN AN ELECTROMAGNETIC FIELD NEAR THE UPPER BOUNDARIES OF SPECTRAL CLUSTERS

摘要

We study the Zeeman-Stark effect in the hydrogen atom located in an electromagnetic field by using irreducible representations of an algebra with the Karasev-Novikova quadratic commutation relations. The representations are associated with resonance spectral clusters near the energy level of the unperturbed hydrogen atom. We find asymp-totics for a series of eigenvalues and corresponding asymptotic eigenfunctions near the upper boundaries of spectral clusters in the case of positive intensities of the electric field.