Quantum nonlinear Schrödinger equation. I: Intertwining operators
type: Item
instance of: scholarly article
title: Quantum nonlinear Schrödinger equation. I: Intertwining operators
zbMATH Open document ID: 0614.35086
DOI: 10.1016/S0294-1449(16)30381-X
author: Eugene Gutkin
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1986-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78115
review text: The quantum nonlinear Schrödinger equation is studied as a model of the quantum (nonrelativistic) field theory in \(1+1\) dimensions. In {\S} 1 the calculus of intertwining operators \(P_ N\), \(P^*_ N\), \(P_ N^{*- 1}\), \(P_ N^{-1}\) on \({\mathcal H}_ N\) is developed which produce the equivalence of the N-particle Hamiltonian \(H_ N\) and the free Hamiltonian \(-\Delta_ N\). In {\S} 2 the intertwining operators on the Fock space are studied, which are the direct sums of the corresponding operators on \({\mathcal H}_ N\). This calculus is supposed to be the basis for subsequent publications on the explicit solution of an initial value problem for the nonlinear Schrödinger equation.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3994158
zbMATH Keywords: delta Bose gas
zbMATH Keywords: Bethe ansatz
zbMATH Keywords: commutation relations
zbMATH Keywords: second quantization
zbMATH Keywords: quantum nonlinear Schrödinger equation
zbMATH Keywords: field theory
zbMATH Keywords: intertwining operators
zbMATH Keywords: Hamiltonian
zbMATH Keywords: Fock space
reviewed by: Joachim Weidmann
MaRDI profile type: Publication
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OpenAlex ID: W2592587979
description: scientific article; zbMATH DE number 3994158