Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields


We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields in near orthogonal configurations. Normalization of the Keplerian symmetry reveals that in the parameter space such systems belong in a ‘zone’ of systems close to the 1:1 resonance, the latter corresponding to the exactly orthogonal configuration. Integrable approximations obtained from second normalization of systems in the 1:1 zone are classified into several different qualitative types, many of which possess nontrivial monodromy. We compute monodromy of the complete three-dimensional energy-momentum map, compare the joint quantum spectrum to classical bifurcation diagrams, and show the effect of second normalization to the joint spectrum.