Eigenvalue and nodal properties on quantum graph trees*

DOI10.1080/17455030600702535zbMath1191.81117OpenAlexW2171498293MaRDI QIDQ3576430

Philipp Schapotschnikow

Publication date: 30 July 2010

Published in: Waves in Random and Complex Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17455030600702535

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items

Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs ⋮ Nodal statistics on quantum graphs ⋮ The nodal count {0,1,2,3,…} implies the graph is a tree ⋮ Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions ⋮ Dynamics of nodal points and the nodal count on a family of quantum graphs ⋮ The number of nodal domains on quantum graphs as a stability index of graph partitions ⋮ An elementary introduction to quantum graphs ⋮ Edge connectivity and the spectral gap of combinatorial and quantum graphs ⋮ Neumann domains on quantum graphs ⋮ A lower bound for nodal count on discrete and metric graphs ⋮ Eigenvalue and nodal properties on quantum graph trees* ⋮ Spectra of regular quantum trees: rogue eigenvalues and dependence on vertex condition ⋮ On the nodal structure of nonlinear stationary waves on star graphs ⋮ Nonlinear Sturm oscillation: From the interval to a star

Cites Work

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• Periodic orbit theory and spectral statistics for quantum graphs
• Inverse Problem for the Sturm--Liouville Equation on a Simple Graph
• Eigenvalue and nodal properties on quantum graph trees*
• Nodal counting on quantum graphs
• Quantum graphs: I. Some basic structures
• Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs