The Calogero-Moser model, the Calogero model and analytic extension.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1033.81044
author: Shuji Watanabe
publication date: 2004-03-29T00:00:00Z
Mathematics Subject Classification ID: 81R12
Mathematics Subject Classification ID: 81V70
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 81U10
zbMATH DE Number: 1664294
zbMATH Keywords: quantum mechanics
zbMATH Keywords: integrability
zbMATH Keywords: exact solutions
zbMATH Keywords: Fourier transform
zbMATH Keywords: two-body Calogero-Moser and Calogero models
MaRDI profile type: Publication
Recommended article: The Quantum Calogero-Moser Model: Algebraic Structures
Recommended article: Integrability and algebraic structure of the quantum Calogero-Moser model
Recommended article: Calogero-Moser space and Kostka polynomials.
Recommended article: Calogero-Moser Models. V: Supersymmetry and Quantum Lax Pair
Recommended article: A generalisation of the Calogero-Moser system
Recommended article: Calogero model(s) and deformed oscillators
Recommended article: Calogero-Moser model and \(R\)-matrix identities
Recommended article: Calogero-Sutherland type models in higher dimensions.
Recommended article: Calogero-Moser systems and representation theory
Recommended article: The Quantum Calogero Model and theW-Algebra
title: The Calogero-Moser model, the Calogero model and analytic extension.
review text: The paper is devoted to a derivation of exact solutions to the Cauchy problem in the two-body Calogero-Moser and Calogero models. Both models are known to be the (one-dimensional) quantum integrable systems describing long-interaction of particles in physics. From the mathematical viewpoint, the solutions found are analytic in time. The author also discusses briefly Wigner's commutation relations in quantum mechanics, as well as the eigenvalue problem of the corresponding Schrödinger equation.NEWLINENEWLINE The generalized Fourier (both cosine and sine) transforms are found explicitly for the exact solutions. The author also discusses at length an embedding theorem of Sobolev type, which appears to be the natural application of the Fourier transform he derived.NEWLINENEWLINE It should be mentioned that similar solutions were derived earlier by \textit{M. Rösler} [ Commun. Math. Phys. 192, 519--542 (1998; Zbl 0908.33005)].NEWLINENEWLINEFor the entire collection see [Zbl 0963.00016].
reviewed by: Sergei V. Ketov
description: scientific article; zbMATH DE number 1664294