Monodromy in the hydrogen atom in crossed fields

Abstract

We show that the hydrogen atom in orthogonal electric and magnetic elds has a special property of certain integrable classical Hamiltonian systems known as monodromy The strength of the elds is assumed to be small enough to validate the use of a 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 eld parameters we show that there is a special dynamically invariant set which is a doubly pinched torus This implies that the integrable Hamiltonian Hsnf has monodromy Manifestation of monodromy in quantum mechanics is also discussed