2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95784We consider the highly anisotropic ferromagnetic spin 1/2 Heisenberg chain with periodic boundary conditions. In each sector of constant total z component of the spin, we develop convergent expansions for the lowest band of eigenvalues and eigenfunctions. These eigenstates describe droplet states in which the spins essentially form a single linear droplet which can move. Our results also give a convergent expansion for the dispersion relation, i.e., the energy of the droplet as a function of its momentum. The methods used are from math-ph/0208026 and cond-mat/0104199, and this short paper should serve as a pedagogic introduction to those papers.submitted to the proceedings of the workshop "Low-energy states in quantum many-body systems", 29 January 2003, Cergy-PontoiseMathematical Physics82B10 (Primary) 82B20 (Secondary)text