# Most typical 1:2 resonant perturbation of the hydrogen atom by weak electric and magnetic fields

K. Efstathiou, O.V. Lukina and D.A. Sadovskií

Phys. Rev. Lett., **101**(25), 253003, 2008

DOI: 10.1103/PhysRevLett.101.253003

## Abstract

We study a perturbation of the hydrogen atom by small homogeneous static
electric and magnetic fields in a specific mutual alignment with angle
approximately π/3 which results in the 1:2 resonance of the linearized
Keplerian *n*-shell approximation. The stratified image of the energy-momentum
map (bifurcation diagram) of the classical integrable approximation has for most
such field configurations the same typical structure which 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
and present also for many near orthogonal field configurations.