Most Typical1∶2Resonant Perturbation of the Hydrogen Atom by Weak Electric and Magnetic Fields

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We study a perturbation of the hydrogen atom by small homogeneous static electric and magnetic fields in a specific mutual alignment with angle approximately pi/3 which results in the 1 ratio 2 resonance of the linearized Keplerian n-shell approximation. The bifurcation diagram of the classical integrable approximation has for most such field configurations the same typical structure that we describe. The structure of the corresponding quantum energy spectrum, which we describe in detail, is in certain ways an analogue of the well-known degeneracy found by Herrick [Phys. Rev. A 26, 323 (1982)] for the quadratic Zeeman effect.