Levinson's theorem for Schroedinger operators with point interaction: a topological approach

TL;DR

This paper derives Levinson's theorems for Schrödinger operators with a point interaction at the origin in R^n using topological methods, specifically winding numbers, and introduces new expressions for wave operators.

Contribution

It provides a novel topological approach to Levinson's theorem for point interactions, including new formulas for wave operators.

Findings

Levinson's theorem is established for Schrödinger operators with point interaction.

Winding numbers are used to relate scattering phase shifts to bound states.

New expressions for wave operators are derived, facilitating the topological proof.

Abstract

In this note Levinson theorems for Schroedinger operators in R^n with one point interaction at 0 are derived using the concept of winding numbers. These results are based on new expressions for the associated wave operators.