2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/22834We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter κdenoting the strength of the harmonic trap. It is shown that the κ\to 0 limit of this problem is singular, in the sense that the density of states for a very shallow trap (κ\to 0) is {\it qualitatively different} from that of a translationally invariant lattice (κ= 0). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.4 pages, 3 figures, REVTEX 4. Three typos corrected and minor textual modificationsStatistical MechanicsSoft Condensed Mattertext