Existence of asymptotic velocity in n-body systems

If H is an N-body Schrödinger operator, then there exists (in an appropriate sense) the limit limt → ∞ eitHxte−itH. This limit defines a vector of self-adjoint operators called the asymptotic velocity. An analogous fact is true in the case of classical N-body systems. We sketch a proof of the existence of the asymptotic velocity.