Three-body pseudopotential for atoms confined in one dimension

Following a strong analogy with two-dimensional physics, the three-body pseudopotential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. The equivalence between this model and the three-body wave equation obtained directly from the Schrödinger equation, including the confinement potential of the waveguide, is demonstrated in the vicinity of the dimer threshold.