# A note on the Exact Green function for a quantum system decorated by two or more impurities

## TL;DR

This paper derives the exact Green function for a quantum system with multiple delta function impurities, revealing how multiple impurities combine into a single effective potential when coinciding, and extending the analysis to N impurities.

## Contribution

It provides a method to construct the exact Green function for systems with multiple impurities and elucidates their behavior when impurities coincide, extending previous single-impurity results.

## Key findings

- Impurities behave as a single potential when coinciding.
- The Green function can be explicitly constructed for multiple impurities.
- Results are extended to systems with N impurities.

## Abstract

The exact Green function is constructed for a quantum system, with known Green function, which is decorated by two delta function impurities.It is shown that when two such impurities coincide they behave as a single singular potential with combined amplitude. The results are extended to N impurities.