Scattering matrices for the quantum N body problem

Let H be a generalized N body Schrodinger operator with very short range po tentials. Using Melrose's scattering calculus, it is shown that the free ch annel 'geometric' scattering matrix, defined via asymptotic expansions of g eneralized eigenfunctions of H, coincides (up to normalization) with the fr ee channel 'analytic' scattering matrix defined via wave operators. Along t he way, it is shown that the free channel generalized eigenfunctions of Her bst-Skibsted and Jensen-Kitada coincide with the plane waves constructed by Hassell and Vasy and if the potentials are very short range.