Does the Bethe-Ansatz Result in a Complete Set of Stationary States for Heisenberg Rings?

The hypothesis is formulated that the Bethe-Ansatz results in a complete set of stationary states for Heisenberg rings if one allows for complex wave numbers k of the deviations from the ferromagnetic "pseudo vacuum" state and for bound pairs of deviations with singular k values. For rings of 2,4,6 and 8 spins the determination of all stationary states confirms the hypothesis for states with 1,2 or 3 deviations.