  In this paper, we compute the diffractive wave propagator of the
Aharonov-Bohm effect on $\mathbf{R}^2$ with a single solenoid using a technique
of moving solenoid location. In addition, we compute the corresponding
diffraction coefficient which is the principal symbol of the diffractive
propagator. This paper gives the first proof of propagation of singularities of
the Aharonov-Bohm Hamiltonian.
