  Extending recent numerical studies on two dimensional amorphous bodies, we
characterize the approach of elastic continuum limit in three dimensional
(weakly polydisperse) Lennard-Jones systems. While performing a systematic
finite-size analysis (for two different quench protocols) we investigate the
non-affine displacement field under external strain, the linear response to an
external delta force and the low-frequency harmonic eigenmodes and their
density distribution. Qualitatively similar behavior is found as in two
dimensions. We demonstrate that the classical elasticity description breaks
down below an intermediate length scale $\xi$, which in our system is
approximately 23 molecular sizes. This length characterizes the correlations of
the non-affine displacement field, the self-averaging of external noise with
distance from the source and gives the lower wave length bound for the
applicability of the classical eigenfrequency calculations. We trace back the
"Boson-peak" of the density of eigenfrequencies (obtained from the velocity
auto-correlation function) to the inhomogeneities on wave lengths smaller than
$\xi$.
