  Future ultrafast x-ray light sources might image ultrafast coherent electron
motion in real-space and in real-time. For a rigorous understanding of such an
imaging experiment, we extend the theory of non-resonant x-ray scattering to
the time-domain. The role of energy resolution of the scattering detector is
investigated in detail. We show that time-resolved non-resonant x-ray
scattering with no energy resolution offers an opportunity to study
time-dependent electronic correlations in non- equilibrium quantum systems.
Furthermore, our theory presents a unified description of ultrafast x-ray
scattering from electronic wave packets and the dynamical imaging of ultrafast
dynamics using inelastic x-ray scattering by Abbamonte and co-workers. We
examine closely the relation of the scattering signal and the linear density
response of electronic wave packets. Finally, we demonstrate that time-resolved
x-ray scattering from a crystal consisting of identical electronic wave packets
recovers the instantaneous electron density.
