Semiclassical Asymptotics of the Spectrum of the Hydrogen Atom in an Electromagnetic Field Near the Upper Boundaries of Spectral Clusters

Abstract

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 asymptotics 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.