We describe a model for s-wave collisions between ground state atoms inoptical lattices, considering especially the limits of quasi-one and twodimensional axisymmetric harmonic confinement. When the atomic interactions aremodelled by an s-wave Fermi-pseudopotential, the relative motion energyeigenvalues can easily be obtained. The results show that except for a boundstate, the trap eigenvalues are consistent with one- and two- dimensionalscattering with renormalized scattering amplitudes. For absolute scatteringlengths large compared with the tightest trap width, our model predicts a novelbound state of low energy and nearly-isotropic wavefunction extending on theorder of the tightest trap width.
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