  Low energy scattering amplitudes for two atoms in one- and two-dimensional
atomic wave guides are derived for short range isotropic and resonant
interactions in high partial wave channels. Taking into account the finite
width of the resonance which was neglected in previous works is shown to have
important implications in the properties of the confinement induced resonances.
For spin polarized fermions in quasi-1D wave guides it imposes a strong
constraint on the atomic density for achieving the Fermi Tonks Girardeau gas.
For a planar wave guide, the charateristics of the 2D induced scattering
resonances in $p$- and d-wave are determined as a function of the 3D scattering
parameters and of the wave guide frequency.
