Comparing the spectrum of Schrödinger operators on quantum graphs

DOI10.1090/proc/16578zbMath1526.34063arXiv2212.13954OpenAlexW4386279688MaRDI QIDQ6083362

Joachim Kerner, Unnamed Author

Publication date: 31 October 2023

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.13954

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Cites Work

• The Maslov index and the spectra of second order elliptic operators
• Differences between Robin and Neumann eigenvalues
• Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples
• Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
• Heat-kernel and Resolvent Asymptotics for Schrodinger Operators on Metric Graphs
• Quantum graphs: I. Some basic structures
• Spectrum of a non-selfadjoint quantum star graph
• The heat kernel on the diagonal for a compact metric graph
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