Exact multi-anyon wave functions in a magnetic field

We present a systematic analysis of the N-body problem for anyons in the presence of an external magnetic field. We find exact N-particle anyonic wave functions which are eigenstates of both energy and angular momentum. We prove the general belief that multi-anyon wave functions fall into two classes. Our wave functions are generated algebraically by the action of symmetrized step operators on two base states. For a generic statistics parameter we identify those combinations of step operators which produce wave functions satisfying the appropriate physical statistics and regularity conditions. For the special case of integer statistics parameter (i.e. bosons or fermions), all combinations are allowed and give all the usual Slater multi-particle states. We also present certain classes of anyonic wave functions in closed functional form.