2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216285We investigate the spectrum and eigenstates of a Bose-Hubbard chain containing two bosons with fixed boundary conditions. In the noninteracting case the eigenstates of the system define a two-dimensional normal-mode space. For the interacting case weight functions of the eigenstates are computed by perturbation theory and numerical diagonalization. We identify paths in the two-dimensional normal-mode space which are rims for the weight functions. The decay along and off the rims is algebraic. Intersection of two paths (rims) leads to a local enhancement of the weight functions. We analyze nonperturbative effects due to the degeneracies and the formation of two-boson bound states.10 pages, 11 figures. With minor corrections. Accepted in Physica DMesoscale and Nanoscale PhysicsOther Condensed Mattertext