2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96227A problem of collisions of atoms with two-channel zero-range interaction in an atomic waveguide is solved by using of a renormalization procedure. A matching of the solution to a solution of the related one-dimensional problem leads to relation between the one-dimensional and three-dimensional scattering parameters. The scattering amplitude and bound states for the confined system demonstrate differences from the related free and one-dimensional systems.Completely rewritten version,8 pages with 5 figures, uses REVTeXStatistical MechanicsSoft Condensed Mattertext