The Aharonov-Bohm scattering problem is solved in a very simple way in parabolic coordinates when eΦ/2πc takes half integers. A modification to the previously presented scattering solution is discussed when eΦ/2πc takes integers.
The Aharonov-Bohm (AB) equation is reformulated by means of the gauge transformation. A scattering theoretical approach yields an integral equation of the form of Kirchhoff-Huygens. The method to solve this equation is analogous to the one previously used to study the dislocation mediated AB effect. It is reconfirmed that the shadow of the magnetic-flux filament appears in the down stream of the electronic flux. Expression for the large angle scattering obtained by AB is improved and the present expression is shown to agree with numerical solution.