Autocorrelation function and quantum recurrence of wavepackets

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Abstract
Quantum wavepackets follow classical orbits and spread initially with time except for the special case when the energy levels are equally spaced, e.g. the harmonic oscillator. However, for integrable systems bound localised wavepackets can exhibit at long times quantum recurrences which do not have a classical correspondence. For the Coulomb potential the recurrence time is approximately n/3 times the Kepler period 2 pi n3, where n is the mean value of the principal quantum numbers of the wavepacket.