Weak convergence of wave values in quantum Heisenberg model
type: Item
instance of: scholarly article
title: Weak convergence of wave values in quantum Heisenberg model
zbMATH Open document ID: 0596.60010
DOI: 10.1016/0034-4877(80)90101-9
author: B. George
published in: Reports on Mathematical Physics
publication date: 1980-01-01T00:00:00Z
review text: In solving the eigenvalue problem for the quantum one-dimensional Heisenberg model, Bethe's hypothesis about the form of the wave function as a permutation of products of plane waves with real wave values plays an essential rôle. To prove uniqueness of Bethe's solution, \textit{C. N. Yang} and \textit{C. P. Yang} [Phys. Rev. 150, 321 ff. (1966)] analysed the properties of the algebraic equations satisfied by the wave values. The author proves the weak convergence of wave values and therefore the existence of thermodynamical limit. The proof of existence of the limit density by using a perturbative procedure is successfully accomplished.
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3960642
zbMATH Keywords: perturbation theory
zbMATH Keywords: eigenvalue problem for the quantum one-dimensional Heisenberg
zbMATH Keywords: model
zbMATH Keywords: weak convergence of wave values
zbMATH Keywords: thermodynamical limit
zbMATH Keywords: eigenvalue problem for the quantum one-dimensional Heisenberg model
reviewed by: Oliviu Gherman
MaRDI profile type: Publication
full work available at URL: 0034-4877(80)90101-9
OpenAlex ID: W2035653403
description: scientific article; zbMATH DE number 3960642