Quantum Physics


Simplified Path Integral Approach to the Aharonov-Bohm Effect

Authors: William O. Straub

In classical electrodynamics the vacuum is defined as a region where there are no electric or magnetic fields. In such a region, a charged particle (such as an electron) will feel no effect — the Lorentz force is zero. The space external to a perfect (i.e., infinite) solenoid can be considered an electromagnetic vacuum, since E and B vanish there. While a non-zero vector potential A does exist outside the solenoid, it can exert no influence on the particle, and thus cannot be directly detected or quantified classically. However, in 1959 Aharonov and Bohm predicted that a vector field would exert a purely quantum-mechanical effect on the phase of the particle’s wave function, which in principle should be detectable. The predicted phase shift was not observed experimentally until 1986, when Tonomura brilliantly verified the effect using a microscopic solenoid. This paper provides a simplified explanation of the Aharonov-Bohm effect using a path-integral approach that is suitable for the advanced undergraduate.

Comments: 6 Pages.

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Submission history

[v1] 2014-03-27 12:09:57

Unique-IP document downloads: 790 times

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