2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/24796We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.RevTex file, 14 pages, 22 figures, published versionStatistical MechanicsOther Condensed Mattertext