An elementary introduction to quantum graphs
Gregory Berkolaiko
TL;DR
This paper provides an accessible introduction to the spectral theory of quantum graphs, illustrating basic tools through examples and applying them to analyze eigenfunction zeros.
Contribution
It offers an elementary exposition of spectral tools for quantum graphs and demonstrates their application to eigenfunction zero counting.
Findings
Basic spectral tools for quantum graphs explained
Eigenfunction zero counts analyzed using these tools
Accessible introduction suitable for newcomers
Abstract
We describe some basic tools in the spectral theory of Schr\"odinger operator on metric graphs (also known as "quantum graph") by studying in detail some basic examples. The exposition is kept as elementary and accessible as possible. In the later sections we apply these tools to prove some results on the count of zeros of the eigenfunctions of quantum graphs.
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