  In present work, we discuss some topological features of charged particles
interacting a uniform magnetic field in a finite volume. The edge state
solutions are presented, as a signature of non-trivial topological systems, the
energy spectrum of edge states show up in the gap between allowed energy bands.
By treating total momentum of two-body system as a continuous distributed
parameter in complex plane, the analytic properties of solutions of finite
volume system in a magnetic field is also discussed.
