The Flux-Across-Surfaces Theorem under conditions on the scattering state

The flux-across-surfaces theorem (FAST) describes the outgoing asymptotics of the quantum flux density of a scattering state. The FAST has been proven for potential scattering under conditions on the outgoing asymptote $\psi_{\text{out}}$ (and of course under suitable conditions on the scattering potential). In this article we prove the FAST under conditions on the scattering state itself. In the proof we will establish also new mapping properties of the wave operators.