The Hamiltonian of the quantum nonlinear Schrodinger equation is a selfadjoint operator on Fock space whose eigenstates are given by the Bethe Ansatz. The quantum inverse scattering method of the physics literature introduced two families of operators which have been claimed to satisfy important properties. Operators of one family are diagonal on the Bethe Ansatz eigenstates, while the other family creates the Bethe Ansatz eigenstates. In the present work we examine these operators. VVe establish some of the claims and show the inconsistency of others.