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 Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 9, Pages 1630–1638 (Mi zvmmf599)

Resonances and trapped modes in a quantum waveguide

A. A. Arsen'ev

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: Properties of the eigenfunctions of the continuous spectrum of a self-adjoint differential second-order operator in a cylinder are investigated. It is proved that the eigenfunctions of the continuous spectrum are analytic with respect to the spectral parameter near the eigenvalues embedded in the continuous spectrum, and any eigenvalue embedded in the continuous spectrum is a removable singular point for the corresponding eigenfunctions.

Key words: resonances and trapped modes, quantum waveguides, eigenvalue problem.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:9, 1573–1581

Bibliographic databases:

UDC: 519.6:517.958:621.378.8

Citation: A. A. Arsen'ev, “Resonances and trapped modes in a quantum waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1630–1638; Comput. Math. Math. Phys., 45:9 (2005), 1573–1581

Citation in format AMSBIB
\Bibitem{Ars05} \by A.~A.~Arsen'ev \paper Resonances and trapped modes in a quantum waveguide \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2005 \vol 45 \issue 9 \pages 1630--1638 \mathnet{http://mi.mathnet.ru/zvmmf599} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216073} \elib{http://elibrary.ru/item.asp?id=13491532} \transl \jour Comput. Math. Math. Phys. \yr 2005 \vol 45 \issue 9 \pages 1573--1581