  We consider the Aharonov-Bohm effect for the Schroedinger operator and the
related inverse problem in an exterior domain the 2-dim. Euclidean space with
Dirichlet boundary condition. We study the structure and asymptotics of
generalized eigenfunctions and show that the scattering operator determines the
domain and the Hamiltonian up to Gauge equivalence under the equal flux
condition. We also show that the flux is determined by the scattering operator
if the obstacle is convex.
