NEW INTEGRABLE SYSTEMS - HYDROGEN-ATOM IN EXTERNAL FIELDS

We report the discovery of two new three-dimensional conservative Hami ltonian systems which are completely integrable. In both cases, two ad ditional integrals of motion in involution are generators of purely dy namical symmetries, i.e., they do not follow from any apparent geometr ical symmetry of the system and are fairly complicated functions of ca nonical coordinates. Physically, the obtained Hamiltonian functions ar e good approximations for the description of the hydrogen atom in a ci rcularly polarized microwave field (for low frequencies) or in crossed magnetic and electric fields (for low magnetic field). More formally, they correspond to the hydrogen atom in the presence of both a circul arly polarized laser field and a generalized Van der Waals potential.