Seminarium KMMF "Teoria Dwoistości"

For a general class of N-body Schrödinger operators with short-rangepair-potentials the wave and scattering matrices as well as the restricted wave operators are quantities given at non-threshold energies. From previous work by Yafaev they are known to exist and to depend weakly continuously on the energy parameter. In the present work we introduce the notion of stationary complete energies and show that all non-threshold energies are stationary complete. It is a consequence of this new result that the above scattering quantities depend strongly continuously on the energy parameter. Another new result is that the scattering matrix is unitary at any non-threshold energy. As side results we obtaina purely stationary proof of asymptotic completeness for N -body short-range systems as well as top-order (far distance) resolvent asymptotics.