Scattering Operator and Wave Operators for 2D Schrödinger Operators with Threshold Obstructions

Abstract

© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.We determine the low-energy behaviour of the scattering operator of two-dimensional Schrödinger operators with any type of obstructions at 0-energy. We also derive explicit formulas for the wave operators in the absence of p-resonances, and outline in this case a topological version of Levinson’s theorem.