Aharonov–Bohm scattering and the velocity operator

It is shown that the existence of Aharonov–Bohm scattering depends upon the criteria used for establishing the stationary states. If one applies Pauli’s criterion, there is no scattering. It is shown further that applying the usual criteria that the wave functions be continuous and single valued, as was done by Aharonov and Bohm, leads to stationary state wave functions which, with two exceptions, are eigenstates of the acceleration operator corresponding to eigenvalue zero. The acceleration operator is undefined for the remaining two states. Thus, only the eigenfunctions satisfying the Pauli criterion lead to well-defined, sensible physics.