2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167175We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.3 pages, 1 figureQuantum PhysicsMathematical Physicstext