2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80488We review the theory for exactly solving quantum Hamiltonian systems through the algebraic Bethe ansatz. We also demonstrate how this theory applies to current studies in Bose-Einstein condensation and metallic grains which are of nanoscale size.23 pages, no figures, to appear in ``Classical and Quantum Nonlinear Integrable Systems'' ed. A. KunduExactly Solvable and Integrable SystemsCondensed Mattertext