ANALYTIC SOLUTION OF A 2-DIMENSIONAL HYDROGEN-ATOM .2. RELATIVISTIC THEORY

In this paper, we derive the exact analytic solution for the relativistic (2 + 1)-dimensional hydrogen atom, both with and without the Chern-Simons field. The atomic spectra without the Chern-Simons field is expanded in powers of the fine-structure constant and compared to the nonrelativistic spectra with the fine-structure splitting, while the Chern-Simons spectrum is investigated in detail for different anomalous angular-momentum values. Fractional statistics and charge are a natural consequence of the Chern-Simons eigenfunctions. The semion (particle with exotic statistical phase factor +/- i) ground state for such a hydrogen atom collapses.