Quantum-mechanical motion of Gaussian wave packets on elliptical and hyperbolic Kepler orbits in the Coulomb field.

The quantum-mechanical motion of Gaussian wave packets on elliptical and hyperbolic orbits is calculated and shown in plots. The approximation scheme makes explicit use of energy and angular-momentum conservation thus guaranteeing controlled accuracy of the approximation over long-time intervals. This allows the study of the revivals, a phenomenon of particular interest in Rydberg atoms on elliptical orbits. A comparison with the behavior of a classical phase-space distribution of the same position and momentum widths is carried out.