Hydrogen atoms placed in external fields serve as a paradigm of a strongly coupled multidimensional Hamiltonian system. This system has been already very extensively studied, using experimental measurements and a wealth of theoretical methods. In this work, we apply the Morales-Ramis theory of non-integrability of Hamiltonian systems to the case of the hydrogen atom in perpendicular (crossed) static electric and magnetic uniform fields.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-12,
author = {Robert G\k ebarowski},
title = {On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {197-204},
zbl = {1234.37043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-12}
}
Robert Gębarowski. On the classical non-integrability of the Hamiltonian system for hydrogen atoms in crossed electric and magnetic fields. Banach Center Publications, Tome 95 (2011) pp. 197-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-12/