Chapter 4: Classical-Quantum Correspondence

Fractional revivals in a hydrogen circular orbit wave packet

The animation shows the motion of a circular orbit wave packet strobed once every Kepler period. The wave packet is a Gaussian superposition of 21 circular states (n=l) centered about n=360. The motion is shown for 120 Kepler periods.

The strobing shows the phenomenon of fractional revivals of the wave packet,when the wavefunction of the electron becomes localized in many separate but coherent wave packets. Note that at a time equal to n/3 times the Kepler period, the wave packet experiences a "full revival", which is 180 degrees out of phase with the original wave packet. More information on the fractional revivals of the circular orbit wave packet can be found in the paper:

Classical and quantum mechanical dynamics of quasiclassical state of a hydrogen atom
Z. Dacic Gaeta and C. R. Stroud, Jr.
Phys. Rev. A 42, 6308-6313 (1990)