Spreading of a hydrogen circular orbit wave packet
The wave packet is initially well-localized but begins to spread because of the unequal spacing between the hydrogenic energy levels. If we had included more than 21 states in the superposition we would have obtained a more localized initial wave packet which would have then spread more quickly.
The corresponding classical ensemble would also show a spreading or "decay" but an important difference between the quantum and classical systems is seen at longer times. Classically, the probability remains spread out around the orbit at later times but quantum mechanically, the finite number frequencies in the problem lead to a rephasing of the wave packet. In fact there are partial rephasings which occur at certain times and we call these fractional revivals.
More information on the decay of the circular orbit wave packet can be found in
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Last modified 13 September 2006