Monodromy in the hydrogen atom in crossed fields

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 Hsnf which is obtained from a two step normalization of the original system. We consider the level sets of Hsnf 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 Hsnf has monodromy. Manifestation of monodromy in quantum mechanics is also discussed. © 2000 Elsevier Science B.V. All rights reserved. PACS: 03.20.+i; 32.60.+i