On the bound states of Schrödinger operators with δ-interactions on conical surfaces

DOI10.1080/03605302.2016.1168843zbMath1346.35139arXiv1510.05623OpenAlexW3105379340MaRDI QIDQ3188106

Vladimir Lotoreichik, Thomas Ourmières-Bonafos

Publication date: 16 August 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.05623

zbMATH Keywords

Schrödinger operatorspectral asymptoticsexistence of bound states\(\delta\)-interactionsconical and hyperconical surfaces

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10)

Related Items (19)

Optimization of the lowest eigenvalue of a soft quantum ring ⋮ Geometrically induced spectral effects in tubes with a mixed Dirichlet-Neumann boundary ⋮ Discrete spectrum of interactions concentrated near conical surfaces ⋮ Asymptotic spectral analysis in colliding leaky quantum layers ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ Aharonov and Bohm versus Welsh eigenvalues ⋮ Spectral asymptotics of the Dirichlet Laplacian on a generalized parabolic layer ⋮ Spectral asymptotics for \(\delta\)-interactions on sharp cones ⋮ Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions ⋮ Leaky quantum structures ⋮ Eigenvalue counting function for Robin Laplacians on conical domains ⋮ Discrete spectrum of Schrödinger operators with potentials concentrated near conical surfaces ⋮ Dirichlet spectrum of the Fichera layer ⋮ Functional difference equations and eigenfunctions of a Schrödinger operator with δ ′ −interaction on a circular conical surface ⋮ A spectral isoperimetric inequality for cones ⋮ Spectral transitions for Aharonov-Bohm Laplacians on conical layers ⋮ Spectral optimization for singular Schrödinger operators ⋮ Optimization of the lowest eigenvalue for leaky star graphs ⋮ Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane

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