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

The Green's functions of the two and three-dimensional relativistic Aharonov-Bohm (A-B) systems are given by the path integral approach. In addition the exact radial Green's functions of the spherical A-B quantum billiard system in two and three-dimensional are obtained via the perturbation techanique of δ-function.