EXACT ANYONIC STATES FOR A GENERAL QUADRATIC HAMILTONIAN

Exact energy eigenstates are produced for the problem of N nonrelativistic anyons with a general rotationally invariant hamiltonian quadratic in coordinates and momenta. In particular, this contains the system of anyons in an external harmonic oscillator potential and a constant magnetic field interacting through two-body linear and magnetic forces. Although an infinite class of states are found, there are "missing" states from the spectrum, whose discovery still remains an open issue.