Classical evolution of quantum elliptic states
Paolo Bellomo and C. R. Stroud, Jr.
Phys. Rev. A 59, 2139 (1999).
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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 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
that have maximum total angular momentum and also maximum projection of the
angular momentum along a fixed direction.
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