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Institute of Optics

Motion of a Circular Orbit Wave Packet

This animation follows the motion of a circular orbit wave packet for 30 Kepler periods (that is, the time needed for a classical electron to orbit 30 times around the nucleus). The wave packet is a Gaussian superposition of 17 circular states centered about n=180.

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.)

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:

Color Wheel


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