Celestial Mechanics on a Microscopic Scale

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Abstract
Classical and semiclassical methods are unrivaled in providing an intuitive and computationally tractable approach to the study of atomic, molecular, and nuclear dynamics. An important advantage of such methods is their ability to uncover in a single picture underlying structures that may be hard to extract from the profusion of data supplied by detailed quantum calculations. Modern trends in semiclassical mechanics are described, particularly the combination of group theoretical methods with techniques of nonlinear dynamics. Application is made to intramolecular energy transfer and to the electronic structure of atomic Rydberg states in external electric and magnetic fields.