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

Abstract

We study the Zeeman-Stark effect problem in the hydrogen atom located in an electromagnetic field by using irreducible representations of the Karasev-Novikova algebra with quadratic commutation relations. We find asymptotics of a series of eigenvalues and the corresponding eigenfunctions near the lower boundaries of spectral clusters. Bibliography: 10 titles. Illustrations: 1 figure.