Rydberg electron dynamics in external fields

We review the role which classical trajectories play in quantum-mechanical systems in a more or less chronological order guided by experimental observations. The onset of a renewed interest in classical dynamics was catalysed by the observation of unknown features in the adsorption spectra of atoms in the presence of external magnetic and electric fields. Although the most dominant features in these spectra can be accounted for by the simple quantisation conditions for classical electrons, the finer details require a more sophisticated approach. Starting from the Feynman path-integral formalism, Gutzwiller's periodic-orbit theory is introduced, which is then transformed into the closed-orbit theory developed by Delos et al. Applying this semiclassical theory enabled atomic physicists to understand complicated quantum spectra as a coherent sum of classical trajectories. Newly observed features such as core-scattered orbits and ghost orbits, necessitated adjustments to the standard closed-orbit theory in order to be able to reproduce these new features. Recent results from both scaled-energy experiments and wave-packet experiments are presented to demonstrate the classical dynamics underlying the quantum system as it is currently understood.