Existence of bound states for layers built over hypersurfaces in \(\mathbb R^{n+1}\)

DOI10.1016/j.jfa.2006.11.017zbMath1111.81059arXivmath/0402252OpenAlexW2100517013MaRDI QIDQ880084

Zhiqin Lu, Christopher Lin

Publication date: 10 May 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402252

zbMATH Keywords

ground stateessential spectrumquantum layer

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Elliptic equations on manifolds, general theory (58J05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (14)

Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces ⋮ Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension ⋮ Compact submanifolds supporting singular interactions ⋮ Asymptotic spectral analysis in colliding leaky quantum layers ⋮ Location of the essential spectrum in curved quantum layers ⋮ Breaking a magnetic zero locus: Asymptotic analysis ⋮ Spectral asymptotics of the Dirichlet Laplacian on a generalized parabolic layer ⋮ Quantum layers over surfaces ruled outside a compact set ⋮ Magnetic effects in curved quantum waveguides ⋮ Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions ⋮ Ruled strips with asymptotically diverging twisting ⋮ Dirac operator spectrum in tubes and layers with a zigzag-type boundary ⋮ On the discrete spectrum of quantum layers ⋮ The magnetic Laplacian in shrinking tubular neighborhoods of hypersurfaces

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