  We derive pseudo-potentials that describe the scattering between two
particles in two spatial dimensions for any partial wave m, whose scattering
strength is parameterized in terms of the m-dependent phase shift. Using our
m=0 pseudo-potential, we develop a coupled channel model with 2D zero-range
interactions, which describes the two-body physics across a Feshbach resonance.
Our model predicts the scattering length, the binding energy and the "closed
channel molecular fraction" of two particles; these observables can be measured
in experiments on ultracold quasi-2D atomic Bose and Fermi gases with
present-day technology.
