Explicit formulas for the Schroedinger wave operators in R^2

TL;DR

This paper derives explicit formulas for Schrödinger wave operators in two-dimensional space, under specific spectral conditions, facilitating the application of topological methods in scattering theory.

Contribution

It provides explicit formulas for wave operators in R^2, supporting the use of topological approaches to scattering theory and index theorems.

Findings

Formulas valid when zero-energy is not an eigenvalue or resonance

Supports topological methods in scattering theory

Enables derivation of index theorems in R^2

Abstract

In this note, we derive explicit formulas for the Schroedinger wave operators in R^2 under the assumption that 0-energy is neither an eigenvalue nor a resonance. These formulas justify the use of a recently introduced topological approach of scattering theory to obtain index theorems.