Mathematical Scattering Theory in Quantum Waveguides

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Abstract

Abstract: A waveguide occupies a domain G with several cylindrical ends. The waveguide is described by a nonstationary equation of the form iმt, where A is a selfadjoint second order elliptic operator with variable coefficients (in particular, for A=-Δ, where Δ stands for the Laplace operator, the equation coincides with the Schrödinger equation). For the corresponding stationary problem with spectral parameter, we define continuous spectrum eigenfunctions and a scattering matrix. The limiting absorption principle provides expansion in the continuous spectrum eigenfunctions. We also calculate wave operators and prove their completeness. Then we define a scattering operator and describe its connections with the scattering matrix.

Original languageEnglish
Pages (from-to)430-433
Number of pages4
JournalDoklady Physics
Volume64
Issue number11
DOIs
StatePublished - 1 Nov 2019

Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)

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