The three-body pseudo-potential for atoms confined in one dimension
Abstract
Following a strong analogy with two-dimensional physics, the three-body pseudo-potential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. In the vicinity of the dimer threshold a direct connection is made between the zero-range potential and the dimensional reduction of the three-body Schr\"odinger equation.
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