Analytic wave functions for understanding the spectrum of the three-anyon problem.
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We show that the low-lying spectrum of three noninteracting anyons in a harmonic potential can be qualitatively and quantitatively understood on the basis of a simple set of analytic wave functions. These wave functions are exact in both the boson and fermion limits and satisfy the anyone wave-function phase condition at all intermediate values of the statistical parameter 0<<1. The resulting nonlinear spectrum agrees with those of exact numerical calculations to better than a few parts in a thousand. 1992 The American Physical Society.