Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window

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dc.creatorExner, P.
dc.creatorVugalter, S. A.
dc.date1996-02-02
dc.date.accessioned2026-07-07T09:13:35Z
dc.date.available2026-07-07T09:13:35Z
dc.descriptionConsider the Laplacian in a straight planar strip of width $\,d\,$, with the Neumann boundary condition at a segment of length $\,2a\,$ of one of the boundaries, and Dirichlet otherwise. For small enough $\,a\,$ this operator has a single eigenvalue $\,ε(a)\,$; we show that there are positive $\,c_1,c_2\,$ such that $\,-c_1 a^4 \le ε(a)- \left(π/ d\right)^2 \le -c_2 a^4\,$. An analogous conclusion holds for a pair of Dirichlet strips, of generally different widths, with a window of length $\,2a\,$ in the common boundary.
dc.descriptionLaTeX file, 12 pages, no figures
dc.identifierhttps://arxiv.org/abs/funct-an/9602001
dc.identifierhttp://arxiv.org/abs/funct-an/9602001
dc.identifierAnn. Inst. H. Poincare 65 (1996), 109-123
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152378
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.titleAsymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window
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