Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields near the Lower Boundaries of Spectral Clusters

Abstract

The Zeeman—Stark effect for the hydrogen atom in an electromagnetic field is considered by using irreducible representations of an algebra with Karasev—Novikova quadratic commutation relations. The asymptotics of the series of eigenvalues and asymptotic eigenfunctions are obtained near the lower boundaries of the resonance spectral clusters, which are formed near the energy levels of the unperturbed hydrogen atom.