  The hydrogen atom in weak external fields is a very accurate model for the
multiphoton excitation of ultrastable high angular momentum Rydberg states, a
process which classical mechanics describes with astonishing precision. In this
paper we show that the simplest treatment of the intramanifold dynamics of a
hydrogenic electron in external fields is based on the elliptic states of the
hydrogen atom, i.e., the coherent states of SO(4), which is the dynamical
symmetry group of the Kepler problem. Moreover, we also show that classical
perturbation theory yields the {\it exact} evolution in time of these quantum
states, and so we explain the surprising match between purely classical
perturbative calculations and experiments. Finally, as a first application, we
propose a fast method for the excitation of circular states; these are
ultrastable hydrogenic eigenstates which have maximum total angular momentum
and also maximum projection of the angular momentum along a fixed direction. %
