Communications in Mathematical Physics

, Volume 154, Issue 2, pp 347–376

Orthogonality and completeness of the Bethe Ansatz eigenstates of the nonlinear Schroedinger model

  • T. C. Dorlas
Article

DOI: 10.1007/BF02097001

Cite this article as:
Dorlas, T.C. Commun.Math. Phys. (1993) 154: 347. doi:10.1007/BF02097001

Abstract

A rigorous proof is given of the orthogonality and the completeness of the Bethe Ansatz eigenstates of theN-body Hamiltonian of the nonlinear Schroedinger model on a finite interval. The completeness proof is based on ideas of C.N. Yang and C.P. Yang, but their continuity argument at infinite coupling is replaced by operator monotonicity at zero coupling. The orthogonality proof uses the algebraic Bethe Ansatz method or inverse scattering method applied to a lattice approximation introduced by Izergin and Korepin. The latter model is defined in terms of monodromy matrices without writing down an explicit Hamiltonian. It is shown that the eigenfunctions of the transfer matrices for this model converge to the Bethe Ansatz eigenstates of the nonlinear Schroedinger model.

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • T. C. Dorlas
    • 1
  1. 1.University College SwanseaSwanseaUK