Monodromy in the hydrogen atom in crossed fields

PHYSICA D-NONLINEAR PHENOMENA

卷:142

Article

Cushman, RH ; Sadovskií, DA

关键词: singular reduction;    monodromy;    energy-momentum map;   

DOI  :  10.1016/S0167-2789(00)00053-1

来源: Elsevier

【 摘 要 】

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 H-snf which is obtained from a two step normalization of the original system. We consider the level sets of H-snf 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 H-snf has monodromy. Manifestation of monodromy in quantum mechanics is also discussed. (C) 2000 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free