The wave packet is initially well-localized but begins to spread after just a few orbits, because of the unequal spacing between the hydrogenic energy levels.

After this spreading, or "decay," the discrete nature of the quantum-mechanical energy levels leads to rephasings of the wave packet. These are called "fractional revivals." The initial wave packet would re-appear at 60 Kepler periods. (Likewise, at 60 / 2 = 30 Kepler periods there are 2 copies of the wave packet, at 60 / 3 = 20 Kepler periods there are 3 copies of the wave packet, and so forth.)

The coloring on this animation indicates the quantum-mechanical dynamical phase of the electron wave function. The following color wheel shows how we can map the complex "phase" of the wave function to a color for a given point of the wave packet:

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Web page maintained by
Hideomi Nihira ( nihira@optics.rochester.edu ).
Last modified 13 September 2006