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

TL;DR

This paper provides a heuristic interpretation of the magnetic Aharonov-Bohm effect, explaining how the magnetic vector potential locally alters the electron's de Broglie wavelength, acting as a quantum phase plate.

Contribution

It introduces a physical mechanism where the vector potential modifies the electron's wavelength, offering a clearer understanding of the phase shift in the Aharonov-Bohm effect.

Findings

The vector potential acts as a quantum phase plate.

Electron wavelength is locally changed by the vector potential.

The phase shift is gauge-invariant and non-dispersive.

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.