An elementary introduction to quantum graphs

Abstract

We describe some basic tools in the spectral theory of Schrödinger 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.

31 pages, 17 figures

References in corpus (3)

• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
• Eigenvalue estimates on quantum graphs
• Non-Weyl Resonance Asymptotics for Quantum Graphs

Cited by in corpus (5)

• Spectral enclosures for non-self-adjoint extensions of symmetric operators
• A spectral duality in graphs and microwave networks
• Zero Measure and Singular Continuous Spectra for Quantum Graphs
• Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics
• Topological Tenfold Classification and the Entanglement of Two Qubits