Quantum Mechanics
Aharonov-Bohm: Introduction

In classical mechanics the motion of a charged particle is not affected by the presence of magnetic fields in regions from which the particle is excluded. Schematic picture of Aharonov-Bohm set-up The motion of classical particles emitted by the source S is not affected by the magnetic field B because the particles can not enter the region of space where the magnetic field is present. For a quantum charged particle there can be an observable phase shift in the interference pattern recorded at the detector D. This phase shift results from the fact that although the magnetic field is zero in the space accessible to the particle, the associated vector potential is not. The phase shift depends on the flux enclosed by the two alternative sets of paths a and b. But the overall envelope of the diffraction pattern is not displaced indicating that no classical magnetic force acts on the particles. The Aharonov-Bohm effect demonstrates that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics.