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 Izv. IMI UdGU, 2006, Issue 1(35), Pages 83–88 (Mi iimi81)

Scattering problem for the one-dimensional discrete Schrödinger operator with a decreasing potential

L. E. Morozova

Udmurt State University, Izhevsk

Abstract: We consider the one-dimensional discrete Schrödinger operator $H_0+V$ acting on the space $l^2(\mathbb{Z}),$ where $V$ is a decreasing potential. The theorem of existence and uniqueness of the corresponding Lippmann–Schwinger equation is proved. We study the asymptotics behaviour of solutions of this equation.

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UDC: 517.958:530.145.6

Citation: L. E. Morozova, “Scattering problem for the one-dimensional discrete Schrödinger operator with a decreasing potential”, Izv. IMI UdGU, 2006, no. 1(35), 83–88

Citation in format AMSBIB
\Bibitem{Mor06} \by L.~E.~Morozova \paper Scattering problem for the one-dimensional discrete Schr\"odinger operator with a decreasing potential \jour Izv. IMI UdGU \yr 2006 \issue 1(35) \pages 83--88 \mathnet{http://mi.mathnet.ru/iimi81}