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Quantum Graphs
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Quantum Graphs Theory and Examples
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
Introduction
Schrödinger equation on a metric graph
Vertex (Matching) Conditions
Secular Determinant
Dirichlet-to-Neumann Map
Sources
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. 10.1090/conm/700 Preprint available: arXiv:1603.07356.