Bound States in Three-dimensional Quantum Electrodynamics with a Chern-Simons Term

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We investigate a bound state problem in three-dimensional quantum electrodynamics with a Chern-Simons term. The Behte-Salpeter equation is formulated for a fermion-anti-fermion system under a ladder approximation. In a large mass expansion, the Schrodinger equation is derived and solved by a numerical method. The wave functions of bound states and the energy eigenvalues are obtained for various values of a topological mass and also a fermion mass. By inspecting the results, we find interesting features of the bounc system: There exists a critical value of the topological mass, beyond which the bound state disappears. As the topological mass decreases, all the energy of the bound states also decrease logarithmically. The Chern-Simons term gives the bound states a repulsive effect.
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