# Zero modes and low-energy resolvent expansion for three dimensional Schrodinger operators with point interactions

## TL;DR

This paper studies the low-energy properties of three-dimensional Schrödinger operators with point interactions, focusing on the resolvent expansion near zero energy and the conditions for zero energy obstructions.

## Contribution

It provides a detailed analysis of the low-energy resolvent expansion and characterizes zero energy obstructions for Schrödinger operators with point interactions in three dimensions.

## Key findings

- Derived the low-energy resolvent expansion for the operators.
- Identified conditions for the occurrence of zero energy obstructions.
- Analyzed the multiplicity of zero energy obstructions.

## Abstract

We investigate the low-energy behavior of the resolvent of Schrodinger operators with finitely many point interactions in three dimensions. We also discuss the occurrence and the multiplicity of zero energy obstructions.