On the Asymptotics of the Spectrum of the Hydrogen Atom in Orthogonal Electric and Magnetic Fields Near the Upper Boundaries of Spectral Clusters

The problem of the Zeemann-Stark effect for the hydrogen atom in electromagnetic fields is considered using the irreducible representations of the Karasev-Novikova algebra with quadratic commutation relations. An asymptotics of the series of eigenvalues and the asymptotic eigenfunctions are obtained near the upper boundaries of resonance spectral clusters which are formed near the energy levels of an unperturbed hydrogen atom.