Approximations of quantum-graph vertex couplings by singularly scaled potentials

zbMath1278.81095arXiv1306.0881MaRDI QIDQ2848012

Stepan S. Manko, Pavel Exner

Publication date: 25 September 2013

Full work available at URL: https://arxiv.org/abs/1306.0881

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Model quantum field theories (81T10) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (6)

Conditions for realizing one-point interactions from a multi-layer structure model ⋮ Quantum graphs: Coulomb-type potentials and exactly solvable models ⋮ Kreı̆n Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One ⋮ Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators ⋮ Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions ⋮ Scale invariant effective Hamiltonians for a graph with a small compact core

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