  We calculate the dynamic structure factor S(k,omega) of liquid Ge (l-Ge) at
temperature T = 1250 K, and of amorphous Ge (a-Ge) at T = 300 K, using ab
initio molecular dynamics. The electronic energy is computed using
density-functional theory, primarily in the generalized gradient approximation,
together with a plane wave representation of the wave functions and ultra-soft
pseudopotentials. We use a 64-atom cell with periodic boundary conditions, and
calculate averages over runs of up to 16 ps. The calculated liquid S(k,omega)
agrees qualitatively with that obtained by Hosokawa et al, using inelastic
X-ray scattering. In a-Ge, we find that the calculated S(k,omega) is in
qualitative agreement with that obtained experimentally by Maley et al. Our
results suggest that the ab initio approach is sufficient to allow approximate
calculations of S(k,omega) in both liquid and amorphous materials.
