Spectral properties of a Hamiltonian of a four-particle system on a lattice
type: Item
instance of: scholarly article
title: Spectral properties of a Hamiltonian of a four-particle system on a lattice
zbMATH Open document ID: 1238.47052
DOI: 10.3103/S1066369X10120030
author: U. R. Shodiev
author: M. Eh. Muminov
published in: Russian Mathematics
publication date: 2011-11-18T00:00:00Z
review text: This paper deals with the Hamiltonian of a system of four arbitrary quantum particles with two-particle contact (noncompact) interaction potentials on a three-dimensional lattice perturbed by three-particle contact potentials. Particularly, it gives the location of the essential spectrum of the Schrödinger operator \(H(K)\) with respect to the values of the total quasi-momentum \(K \in [-\pi, \pi)^3\) corresponding to a four-particle system. After determination of possible sub-Hamiltonians of a four-particle system and decomposition of the sub-Hamiltonians into direct integral, the essential spectrum of the operator \(H(K)\) is described as the union of the spectra of the sub-Hamiltonians.
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 37K60
zbMATH DE Number: 5975424
zbMATH Keywords: 4-particle Hamiltonian
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: essential spectrum
zbMATH Keywords: compact operator
MaRDI profile type: Publication
cites work: Q3976402
cites work: Q5734302
cites work: Q5516832
cites work: Q3756011
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cites work: Spectrum of a model operator in the perturbation theory of the essential spectrum
cites work: Q4185363
full work available at URL: s1066369x10120030
OpenAlex ID: W1966718004
description: scientific article; zbMATH DE number 5975424