Reflection Probabilities of One-Dimensional Schrödinger Operators and Scattering Theory

Abstract

Abstract. The dynamic reflection probability of [DS] and the spectral reflection probability of [GNP,GS4] for a one-dimensional Schrödinger operator H "´∆`V are characterized in terms of the scattering theory of the pair pH, H 8 q where H 8 is the operator obtained by decoupling the left and right half-lines R ď0 and R ě0 . An immediate consequence is that these reflection probabilities are in fact the same, thus providing a short and transparent proof of the main result of [BRS]. This approach is inspired by recent developments in non-equilibrium statistical mechanics of the electronic black box model and follows a strategy parallel to [JLPa].