The spectrum of a general three-particle lattice Hamiltonian
type: Item
instance of: scholarly article
title: The spectrum of a general three-particle lattice Hamiltonian
zbMATH Open document ID: 0892.47072
DOI: 10.1007/BF02509454
author: Yu. V. Zhukov
publication date: 1997-04-15T00:00:00Z
review text: The author considers three interacting particles moving on a lattice \(\mathbb{Z}^\nu\). Under some assumptions for \(H_0\) and \(V\), it is shown that, for a sufficiently small \(\varepsilon\) and \(\nu\geq 3\), the Hamiltonian \(H(\varepsilon)= H_0+\varepsilon V\) is unitarily equivalent to the free Hamiltonian \(H_0\). This result is similar to the well-known Iorio-O'Carroll theorem for a system of interacting quantum particles moving in \(\mathbb{R}^\nu\) [\textit{M. Reed} and \textit{B. Simon}, Methods of modern mathematical physics, Vol. 3, Scattering theory (Academic Press, New York) (1979; Zbl 0405.47007); Vol. 4, Analysis of operators (Academic Press, New York) (1978; Zbl 0401.47001)].
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81U10
zbMATH DE Number: 999676
zbMATH Keywords: three-body problem
zbMATH Keywords: lattice Hamiltonian
zbMATH Keywords: Iorio-O'Carroll theorem
reviewed by: Werner Stulpe
MaRDI profile type: Publication
cites work: Q4185363
cites work: Q3752126
cites work: Q4698524
full work available at URL: https://doi.org/10.1007/bf02509454
OpenAlex ID: W2078045807
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 999676