  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.
