Analytic solution of a two-dimensional hydrogen atom. II. Relativistic theory

Publisher Website
Google Scholar
Abstract
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.