Semiclassical asymptotics of the spectrum of the hydrogen atom in an electromagnetic field near the upper boundaries of spectral clusters
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.