TY - JOUR

T1 - Mathematical Scattering Theory in Quantum Waveguides

AU - Plamenevskii, B. A.

AU - Poretskii, A. S.

AU - Sarafanov, O. V.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85077050076&partnerID=8YFLogxK

U2 - 10.1134/S102833581911003X

DO - 10.1134/S102833581911003X

M3 - Article

AN - SCOPUS:85077050076

VL - 64

SP - 430

EP - 433

JO - Doklady Physics

JF - Doklady Physics

SN - 1028-3358

IS - 11

ER -