We consider a regularized Wigner equation with an oscillatory kernel,
the regularization acts in the space variable to damp high
frequencies. The oscillatory kernel is directly derived from the
Schr\"odinger equation with an oscillatory potential. The problem
therefore contains three scales, $\eps$ the oscillation length,
$\theta$ the regularization parameter, $\delta$ the potential lattice.
¶ We prove that the homogenized limit (as $\eps$ vanishes) of this
equation is a scattering equation with discrete jumps. As $\delta$
vanishes, the discrete scattering kernel boils down to a standard
regular scattering kernel. As $\theta$ vanishes we recover the quantum
scattering operator with collisions preserving energy sphere.