Article

Monodromy in the hydrogen atom in crossed fields

Mathematics Institute, University of Utrecht, Budapestlaan 6, 3508 TA Utrecht, The Netherlands; Université du Littoral, Citadelle, Boîte Postale 5526, 59379 Dunkirk, France
Physica D: Nonlinear Phenomena DOI:10.1016/S0167-2789(00)00053-1 pp.166-196

ABSTRACT We show that the hydrogen atom in orthogonal electric and magnetic fields has a special property of certain integrable classical Hamiltonian systems known as monodromy. The strength of the fields is assumed to be small enough to validate the use of a truncated normal form which is obtained from a two step normalization of the original system. We consider the level sets of on the second reduced phase space. For an open set of field parameters we show that there is a special dynamically invariant set which is a “doubly pinched 2-torus”. This implies that the integrable Hamiltonian has monodromy. Manifestation of monodromy in quantum mechanics is also discussed.

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Keywords

certain integrable classical Hamiltonian systems
 
integrable Hamiltonian
 
level sets
 
orthogonal electric
 
phase space
 
quantum mechanics
 
special property
 
truncated normal form
 
two step normalization
 

R.H. Cushman