Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\)

DOI10.1007/S00023-016-0532-3zbMath1378.81026arXiv1601.06433OpenAlexW3124573988WikidataQ59529267 ScholiaQ59529267MaRDI QIDQ529602

Jonathan Rohleder, Jussi Behrndt, Vladimir Lotoreichik, Christian Kühn, Rupert L. Frank

Publication date: 19 May 2017

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06433

zbMATH Keywords

Schrödinger operatornegative spectrumscattering matrixabsolutely continuous spectrum\(\delta\)-interactions supported on curvesscattering pair

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Operations with distributions and generalized functions (46F10) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Schrödinger operator, Schrödinger equation (35J10) (S)-matrix theory, etc. in quantum theory (81U20)

Related Items (8)

The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies ⋮ Scattering matrices and Weyl functions of quasi boundary triples ⋮ Spectral isoperimetric inequalities for singular interactions on open arcs ⋮ On Nelson-type Hamiltonians and abstract boundary conditions ⋮ A spectral isoperimetric inequality for cones ⋮ Optimization of the lowest eigenvalue for leaky star graphs ⋮ Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane ⋮ Bound states asymptotics in the system with quantum wires in ℝ³

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