THE NATURE OF THE 3-ANYON WAVE-FUNCTIONS

We show how to separate variables in the problem of three anyons with a harmonic oscillator potential. The anyonic symmetry conditions from cyclic permutations are separable in our coordinates. The conditions f rom two-particle transpositions are not separable, but can be expresse d as reflection symmetry conditions on the wave function and its norma l derivative on the boundary of a circle. We solve this one-dimensiona l problem numerically by discretization.