  We propose a simple way to determine the periodicities of wave packets in
quantum systems directly from the energy differences of the states involved.
The resulting classical periods and revival times are more accurate than those
obtained with the traditional expansion of the energies about the central
quantum number n, especially when n is low. The latter type of wave packet
motion occurs upon excitation of highly charged ions with short XUV or X-ray
pulses. Moreover, we formulate the wave packet dynamics in such a form that it
directly reveals the origin of phase shifts in the maxima of the
autocorrelation function. This phenomenon, so far poorly understood since it is
not prominent in the high n regime, becomes a dominant feature in low n wave
packet dynamics.
