The Aharonov-Bohm wave and the Cornu spiral

For flux , the Aharonov-Bohm wavefunction AB ( r , ) is represented exactly in terms of Fresnel integrals. Numerical evidence shows that in the complex AB plane the wave clings to the Cornu spiral for all positions r except very close to the flux line, that is, the argument w ( r , ) of the Fresnel integrals is almost real. This is confirmed by deriving an asymptotic expansion for w in powers of 1/ r .