Exact Aharonov-Bohm wavefunction obtained by applying Dirac's magnetic phase factor

A solution of Schrodinger's equation for a particle in a magnetic field B can be obtained from the wavefunction when B=0 by Dirac's prescription of multiplication by a phase factor. But this solution is often multiple-valued and hence unsatisfactory. It is shown that in the case of the Aharonov-Bohm effect the Dirac prescription can nevertheless be made to yield the single-valued exact wavefunction, provided it is applied not to the total wave with B=0 but to its separate components in a 'whirling-wave' representation. The mth whirling wave at a point r is a contribution that has arrived at r after travelling m times around the region containing B.