Magnetic Aharonov-Bohm effects and the quantum phase shift: A heuristic interpretation

Abstract

The shift in Aharanov-Bohm electron-interference fringe positions has been previously derived as resulting from phase differences induced by the magnetic vector potential, without being clear on the physical mechanism behind it. In this paper, we show that the de Broglie wavelength of the electron wavefunction is changed locally by its interaction with the vector potential. The vector potential thus acts as a quantum "phase plate", changing the phase difference between interfering electron wavefunctions in a non-dispersive, gauge-invariant manner.