Monodromy in perturbed Kepler systems: Hydrogen atom in crossed fields
Mathematics Institute, University of Utrecht -
3508 TA Utrecht, The Netherlands
2 Université du Littoral - BP 5526, 59379 Dunkerque Cedex, France
Accepted: 21 April 1999
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.
PACS: 03.20.+i – Classical mechanics of discrete systems: general mathematical aspects / 03.65.Sq – Semiclassical theories and applications / 32.60.+i – Zeeman and Stark effects
© EDP Sciences, 1999