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This article is cited in 5 scientific papers (total in 5 papers)
Brief communications
On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator
S. A. Albeverioa, S. N. Lakaevb, Zh. I. Abdullaevb a University of Bonn, Institute for Applied Mathematics
b A. Navoi Samarkand State University
Abstract:
A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.
Keywords:
Schrödinger equation, boson, Faddeev integral equation.
Received: 20.03.2000
Citation:
S. A. Albeverio, S. N. Lakaev, Zh. I. Abdullaev, “On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 56–60; Funct. Anal. Appl., 36:3 (2002), 212–216
Linking options:
https://www.mathnet.ru/eng/faa204https://doi.org/10.4213/faa204 https://www.mathnet.ru/eng/faa/v36/i3/p56
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