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

TL;DR

This paper proves the flux-across-surfaces theorem (FAST) for quantum scattering states under new conditions directly on the scattering state, expanding the theorem's applicability beyond previous asymptotic conditions.

Contribution

The paper introduces a proof of the FAST based on conditions on the scattering state itself and establishes new mapping properties of wave operators.

Findings

Proved FAST under conditions on the scattering state

Established new mapping properties of wave operators

Extended applicability of FAST to broader scattering scenarios

Abstract

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.