MULTI-ANYON QUANTUM-MECHANICS AND FRACTIONAL STATISTICS

We study a many-body system consisting of N identical anyons in an external harmonic oscillator potential. We obtain its (partial) analytic solutions by using Jacobi coordinates. Our study sheds considerable light on symmetrization of anyon wave functions, and it also suggests that the anyon wave functions may be generally constructed from the one-body wave functions, by considering the statistical symmetries as is conventional for bosonic and fermionic systems. To see this, we explicitly construct two families of anyon wave functions and energy spectra in terms of those for fermions and bosons.