Two anyons in a static, uniform magnetic field. Exact solution

The exact solution of the problem of two identical, charged anyons moving in a plane under the influence of a static uniform magnetic field perpendicular to that plane and of the Coulomb repulsion of each other is found. It has been shown that there are bound states only for certain discrete values of the magnetic field. A continuous transition from the boson to the fermion spectrum occurs in the absence as well as in the presence of the Coulomb repulsion. (orig.)