On the point and continuous spectra for coupled quantum waveguides and resonators

DOI10.1016/S0034-4877(97)85901-0zbMath0905.47060OpenAlexW2098961041MaRDI QIDQ1387128

Igor Yu. Popov

Publication date: 10 January 1999

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(97)85901-0

zbMATH Keywords

Dirichlet boundary conditionsNeumann boundary conditionsdispersion equationselfadjoint extensions of symmetric operatorstrapped modesresonatoreigenvalues imbedded in the continuous spectrumeigenvalues imbedded in the waveguiderestriction-extension procedurezero-range potential approach

Mathematics Subject Classification ID

Model quantum field theories (81T10) Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Dilations, extensions, compressions of linear operators (47A20) Applications of quantum theory to specific physical systems (81V99)

Related Items (6)

Asymptotics of bound states and bands for laterally coupled waveguides and layers ⋮ Asymptotics of bound state for laterally coupled waveguides. ⋮ Resonances for laterally coupled quantum waveguides ⋮ Zero-range potential model for a waveguide in photonic crystal ⋮ Violation of symmetry in the system of three laterally coupled quantum waveguides, and resonance asymptotics ⋮ Vladimir A. Geyler

Cites Work

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• Eigenvalues and bands imbedded in the continuous spectrum for a system of resonators and a waveguide: Solvable model
• Trapped modes in open channels
• The theory of extensions and explicitly-soluble models
• The resonator with narrow slit and the model based on the operator extensions theory
• Existence theorems for trapped modes
• Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window

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