Scattering operator and wave operators for 2D Schr\"odinger operators with threshold obstructions

TL;DR

This paper analyzes the low-energy scattering behavior of 2D Schrödinger operators with threshold obstructions, providing explicit formulas for wave operators and a topological perspective on Levinson's theorem.

Contribution

It offers a detailed analysis of scattering and wave operators for 2D Schrödinger operators with threshold obstructions, including explicit formulas and a topological interpretation.

Findings

Explicit formulas for wave operators without p-resonances

Topological version of Levinson's theorem derived

Characterization of low-energy scattering behavior with obstructions

Abstract

We determine the low-energy behaviour of the scattering operator of two-dimensional Schr\"odinger 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.