Quantum Graphs
Quantum Graphs
Theory and Examples
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This is a book devoted to the spectral theory of Schrödinger operator on metric graphs (also known as "quantum graphs"). Every theoretical concept is to be illustrated by studying in detail several examples. The exposition is to be kept as elementary and accessible as possible.
Table of Contents
edit- Introduction
- Schrödinger equation on a metric graph
- Vertex (Matching) Conditions
- Secular Determinant
- Dirichlet-to-Neumann Map
Sources
edit- Berkolaiko, Gregory. "An elementary introduction to quantum graphs". In "Geometric and Computational Spectral Theory" (eds: A. Girouard, D. Jakobson, M. Levitin, N. Nigam, I. Polterovich and F. Rochon), Contemp. Math. 700, AMS, 2017. Amer. Math. Soc. doi:10.1090/conm/700. Preprint available: arXiv:1603.07356.