Quantum Graphs via Exercises

TL;DR

This paper offers a collection of questions and exercises designed to complement existing literature and courses on quantum graphs, aiding in understanding their spectral theory and applications.

Contribution

It provides a structured set of exercises based on courses taught by the authors, enhancing educational resources for quantum graph studies.

Findings

Exercises facilitate learning of spectral theory

Enhances understanding of quantum graphs

Supports existing educational materials

Abstract

Studying the spectral theory of Schroedinger operator on metric graphs (also known as quantum graphs) is advantageous on its own as well as to demonstrate key concepts of general spectral theory. There are some excellent references for this study such as a mathematically oriented book by Berkolaiko and Kuchment, a review with applications to theoretical physicsby Gnutzmann and Smilansky, and elementary lecture notes by Berkolaiko. Here, we provide a set of questions and exercises which can accompany the reading of these references or an elementary course on quantum graphs. The exercises are taken from courses on quantum graphs which were taught by the authors.