  We show the existence and orthogonality of wave operators naturally
associated to a compatible Laplacian on a complete manifold with a corner of
codimension 2. In fact, we prove asymptotic completeness i.e. that the image of
these wave operators is equal to the space of absolutely continuous states of
the compatible Laplacian. We achieve this last result using time dependent
methods coming from many-body Schr\"odinger equations.
