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- Title
Mathematical Scattering Theory in Quantum Waveguides.
- Authors
Plamenevskii, B. A.; Poretskii, A. S.; Sarafanov, O. V.
- Abstract
A waveguide occupies a domain G with several cylindrical ends. The waveguide is described by a nonstationary equation of the form , where is a selfadjoint second order elliptic operator with variable coefficients (in particular, for , 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.
- Subjects
QUANTUM scattering; ELLIPTIC operators; S-matrix theory; SCATTERING (Mathematics); SCHRODINGER equation; SCHRODINGER operator; EIGENFUNCTIONS
- Publication
Doklady Physics, 2019, Vol 64, Issue 11, p430
- ISSN
1028-3358
- Publication type
Article
- DOI
10.1134/S102833581911003X