  We consider potential scattering theory of a nonrelativistic quantum
mechanical 2-particle system in R^2 with anyon statistics. Sufficient
conditions are given which guarantee the existence of wave operators and the
unitarity of the S-matrix. As examples the rotationally invariant potential
well and the delta-function potential are discussed in detail. In case of a
general rotationally invariant potential the angular momentum decomposition
leads to a theory of Jost functions. The anyon statistics parameter gives rise
to an interpolation for angular momenta analogous to the Regge trajectories for
complex angular momenta. Levinson's theorem is adapted to the present context.
In particular we find that in case of a zero energy resonance the statistics
parameter can be determined from the scattering phase.
