The Aharonov-Bohm wave and the Cornu spiral

For flux alpha, the Aharonov-Bohm wavefunction Psi(AB)(r, alpha) is represe nted exactly in terms of Fresnel integrals. Numerical evidence shows that i n the complex Psi(AB) plane the wave clings to the Cornu spiral for all pos itions r except very close to the flux line, that is, the argument omega(r, alpha) of the Fresnel integrals is almost real. This is confirmed by deriv ing an asymptotic expansion for w in powers of 1/r.