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We propose a simple way to determine the periodicities of wave packets inquantum systems directly from the energy differences of the states involved.The resulting classical periods and revival times are more accurate than thoseobtained with the traditional expansion of the energies about the centralquantum number n, especially when n is low. The latter type of wave packetmotion occurs upon excitation of highly charged ions with short XUV or X-raypulses. Moreover, we formulate the wave packet dynamics in such a form that itdirectly reveals the origin of phase shifts in the maxima of theautocorrelation function. This phenomenon, so far poorly understood since it isnot prominent in the high n regime, becomes a dominant feature in low n wavepacket dynamics.

Electronic excitation by short X-ray pulses: From quantum beats to wave packet revivals