Low-Lying Eigenstates of the One-Dimensional Heisenberg Ferromagnet for any Magnetization and Momentum

I present the exact dispersion relations for certain low-lying states of the one-dimensional Heisenberg ferromagnet. These states are bound complexes of $M$ overturned spins, and in fact are the states with the lowest energy for given values of the total spin, $z$ component of spin and momentum.