MONODROMY IN PERTURBED KEPLER SYSTEMS: HYDROGEN ATOM IN CROSSED FIELDS
R. H. Cushman
Mathematics Institute, University of Utrecht,
Budapestlaan 6, 3508 TA Utrecht, The Netherlands
D. A. Sadovski\'\i
Universit\'e du Littoral, BP 5526, 59379 Dunkerque Cedex, France
21 December 1998, in final form 21 April 1999
PACS: 03.20+i Classical mechanics of discrete systems
03.65Sq Semiclassical theories and applications
32 60+i Zeeman and Stark effects
We demonstrate that an integrable approximation to the hydrogen atom in
orthogonal electric and magnetic fields has monodromy, a fundamental dynamical
property that makes a global definition of action-angle variables and of
quantum numbers impossible. When the field strengths are sufficiently small,
we find our integrable approximation using a two step normalization procedure.
One of dynamically invariant sets of the resulting integrable system is a
doubly pinched torus whose existence proves the presence of monodromy.
Europhysics Letters 47(1), 1-7 (1999)