Scattering operator and wave operators for 2D Schrödinger operators with threshold obstructions

Abstract

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.

Revised version. To appear in Complex Analysis and Operator Theory

References in corpus (5)

• Levinson's theorem for Schroedinger operators with point interaction: a topological approach
• Two dimensional Schr{\" o}dinger operators with point interactions: threshold expansions, zero modes and $L^p$-boundedness of wave operators
• On the structure of the wave operators in one dimensional potential scattering
• On the $L^p$ boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions
• $L^p$-boundedness of wave operators for 2D Schrödinger operators with point interactions