The Aharonov-Bohm effect: the role of tunneling and associated forces

Through tunneling, or barrier penetration, small wavefunction tails can enter a finitely shielded cylinder with a magnetic field inside. When the shielding increases to infinity, the Lorentz force goes to zero together with these tails. However, it is shown, by considering the radial derivative of the wavefunction on the cylinder surface, that a flux-dependent force remains. This force explains in a natural way the Aharonov-Bohm effect in the idealized case of infinite shielding.