This classical motion has been observed experimentally and although this state does not represent the ideal classical atom it does help us to understand the differences between the quantum and classical models. The appropriate classical model of the wave packet is not just a single classical electron but an ensemble of electrons moving together as shown above. The quantum wave packet starts out localized near the core and we model this with an ensemble of classical electrons at the inner turning points of their orbits. At half of an orbital (or Kepler) period later the quantum shell of probability is far from the nucleus and the corresponding classical ensemble is at its outer turning point.

There is much more to the story than this. Although the radial wave packet does behave classically for a short period of time, at later times its behaviour has very non-classical characteristics (see our animations section for a little more on this, in the context of the hydrogen circular orbit wave packets). Our purpose was to make the most classical atom possible but we never claimed that its correspondence to a true classical atom would be exact.

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Hideomi Nihira ( nihira@optics.rochester.edu ).
Last modified 13 September 2006