Scattering on Leaky Wires in Dimension Three

Pavel Exner () and Sylwia Kondej ()
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Pavel Exner: Nuclear Physics Institute, Czech Academy of Sciences
Sylwia Kondej: Institute of Physics, University of Zielona Góra

A chapter in Analysis and Operator Theory, 2019, pp 81-91 from Springer

Abstract: Abstract We consider the scattering problem for a class of strongly singular Schrödinger operators in $$L^2({\mathbb R}^3)$$ L 2 ( R 3 ) which can be formally written as $$H_{\alpha ,\varGamma }= -\varDelta + \delta _\alpha (x-\varGamma )$$ H α , Γ = - Δ + δ α ( x - Γ ) , where $$\alpha \in {\mathbb R}$$ α ∈ R is the coupling parameter and $$\varGamma $$ Γ is an infinite curve which is a local smooth deformation of a straight line $$\varSigma \subset {\mathbb R}^3$$ Σ ⊂ R 3 . Using Kato–Birman method, we prove that the wave operators $$\varOmega _\pm (H_{\alpha ,\varGamma }, H_{\alpha ,\varSigma })$$ Ω ± ( H α , Γ , H α , Σ ) exist and are complete.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-12661-2_6

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DOI: 10.1007/978-3-030-12661-2_6

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