STRONG-COUPLING ASYMPTOTIC EXPANSION FOR SCHRÖDINGER OPERATORS WITH A SINGULAR INTERACTION SUPPORTED BY A CURVE IN ℝ3

DOI10.1142/S0129055X04002084zbMath1053.81030arXivmath-ph/0303033MaRDI QIDQ4818920

Sylwia Kondej, Pavel Exner

Publication date: 24 September 2004

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0303033

zbMATH Keywords

Schrödinger operatorsdiscrete spectrumquantum wiresstrong coupling asymptotic expansion

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (13)

Geometrically induced spectral effects in tubes with a mixed Dirichlet-Neumann boundary ⋮ Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators ⋮ Weakly coupled bound state of 2-D Schrödinger operator with potential-measure ⋮ SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS ⋮ Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction ⋮ Schrödinger operator with a strong varying interaction on a curve in $\mathbb {R}^2$R2 ⋮ Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\) ⋮ A Klein-Gordon particle captured by embedded curves ⋮ Self-adjointness and spectral properties of Dirac operators with magnetic links ⋮ Infinitely many singular interactions on noncompact manifolds ⋮ On eigenvalue asymptotics for strong δ-interactions supported by surfaces with boundaries ⋮ On the spectrum of curved planar waveguides ⋮ Bound states asymptotics in the system with quantum wires in ℝ³

Cites Work

• Unnamed Item
• Schrödinger operators with singular interactions
• Point interactions in a strip
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Boundary conditions on curves for the three-dimensional Laplace operator
• Curvature-induced bound states for a \(\delta\) interaction supported by a curve in \(\mathbb{R}^3\)
• Geometrically induced spectrum in curved leaky wires
• Bound states in curved quantum waveguides
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• A Krein-like formula for singular perturbations of self-adjoint operators and applications
• Band gap of the Schrödinger operator with a strong \(\delta\)-interaction on a periodic curve

This page was built for publication: STRONG-COUPLING ASYMPTOTIC EXPANSION FOR SCHRÖDINGER OPERATORS WITH A SINGULAR INTERACTION SUPPORTED BY A CURVE IN ℝ³