Motion of a Circular Orbit Wave Packet
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.)
More information on the decay 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).
This animation was originally published (in QuickTime format) in the paper:
Shaping an atomic electron wave packet
Michael W. Noel and C. R. Stroud, Jr.
Optics Express 1, 176 (1997).
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Hideomi Nihira ( email@example.com ).
Last modified 13 September 2006