High Rydberg States of an Atom in a Strong Magnetic Field

Classical trajectories and semiclassical eigenvalues are calculated for an atomic Rydberg state in a magnetic field. Perturbation theory describes a classical trajectory as a Kepler ellipse which rocks, tilts, and flips in space as orbital parameters evolve slowly in time. Exact numerical calculations verify the accuracy of perturbation theory for $n\simeq 30$, $B<~6$ T. Action variables are calculated from perturbation theory and from exact trajectories, and semiclassical eigenvalues obtained by quantization of the action. Good agreement is found with observations.