  The essence of the Thomas-Fermi model is the assumption that the local
behavior of a many-body system can be approximated by that of a homogeneous
system. In this paper, we present the natural extension of the static
Thomas-Fermi treatment of dilute Bose condensates, by describing the dynamical
behavior of the condensate in the same quasi-homogeneous approximation. In
particular, we calculate the dynamical structure factor $S(q, \omega)$ of a
low-temperature condensate, confined in a harmonic oscillator trap. The result
is a remarkably simple analytical function, which, with the proper
interpretation, gives a powerful and insightful description of the scattering
properties of the BEC-system.
