It has been known for a long time that any attractive two-dimensional potential with circular symmetry has a bound state. A simple generalisation of standard scattering theory to two dimensions shows that all cross sections diverge at zero energy; furthermore a T matrix theory can show that those two results are connected, that they correspond to the same kinematical singularity and that they exist for non-circular potentials.
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P. Averbuch (1986) studied this question.
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