On the number of negative eigenvalues of the Laplacian on a metric graph

DOI10.1088/1751-8113/43/47/474006zbMath1204.81076OpenAlexW2008869679MaRDI QIDQ3065967

Jussi Behrndt, Annemarie Luger

Publication date: 7 January 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/342e92c780f4bf12ba65a5527e577769c32e96ac

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (17)

Bounds on the negative eigenvalues of Laplacians on finite metric graphs ⋮ Scattering theory for the matrix Schrödinger operator on the half line with general boundary conditions ⋮ Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge ⋮ The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions ⋮ The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions ⋮ Many-Particle Quantum Graphs: A Review ⋮ Non-compact quantum graphs with summable matrix potentials ⋮ Gluing graphs and the spectral gap: a Titchmarsh–Weyl matrix-valued function approach ⋮ High-energy analysis and Levinson's theorem for the selfadjoint matrix Schrödinger operator on the half line ⋮ Maximal quasi-accretive Laplacians on finite metric graphs ⋮ Many-particle quantum graphs and Bose-Einstein condensation ⋮ \(L^p-L^{p'}\) estimates for matrix Schrödinger equations ⋮ Two interacting particles on the half-line ⋮ The Schrödinger equation on a star-shaped graph under general coupling conditions ⋮ Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions ⋮ The \(L^p\) boundedness of the wave operators for matrix Schrödinger equations ⋮ Wave and scattering operators for the nonlinear matrix Schrödinger equation on the half-line with a potential

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