Semiclassical spectrum of the Schrödinger operator on a geometric graph

DOI10.1134/S0001434607090313zbMath1160.47022OpenAlexW2063081717MaRDI QIDQ942085

Andrej I. Shafarevich, Vsevolod L. Chernyshev

Publication date: 3 September 2008

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434607090313

zbMATH Keywords

asymptoticsspectrumLaplace operatorSturm-Liouville problemgeometric graphone-dimensional Schrödinger operatorBetti number

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Linear symmetric and selfadjoint operators (unbounded) (47B25) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (5)

Statistics of Gaussian packets on metric and decorated graphs ⋮ Time-dependent Schrödinger equation: statistics of the distribution of Gaussian packets on a metric graph ⋮ The semiclassical limit on a star-graph with Kirchhoff conditions ⋮ Semiclassical eigenfunctions of the Schrödinger operator on a graph that are localized near a subgraph ⋮ On hemodynamics problems on graphs

Cites Work

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• Convergence of spectra of graph-like thin manifolds
• Scattering problems on noncompact graphs
• Importance of shadowing and multiple reflections in emission polarization
• Inverse spectral problem for quantum graphs

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