QUANTUM-MECHANICAL MOTION OF GAUSSIAN WAVE-PACKETS ON ELLIPTIC AND HYPERBOLIC KEPLER ORBITS IN THE COULOMB FIELD

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