Rigorous Bethe Ansatz for the Nonlinear Schroedinger Model

Abstract

The author’s recent proof of the completeness and orthogonality of the Bethe Ansatz eigenstates of the nonlinear Schroedinger model is outlined. The complete ness follows from monotonicity in the coupling parameter of the model combined with orthogonality of the Bethe Ansatz eigenfunctions. The latter follows from the orthog onality of the corresponding eigenstates of a lattice approximation to the nonlinear Schroedinger model introduced by Korepin and Izergin. This, in turn follows from the fact that these states are simultaneous eigenstates of a complete set of commuting “transfer operators”, i.e. the fact that the model is completely integrable.