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Of course it is intriguing. But I think the Schroedinger equation for a charged particle in a magnetic field was known at the very beginning of wave mechanics. Therefore, the A-B effect should not be more exotic than the Schroedinger equation.

A-B effect is simply an immediate consequence of the Schroedinger equation. So why was it debatable?

Qmechanic
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Jiang-min Zhang
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    In the Aharonov–Bohm effect, the magnetic field is zero along the electrons path. So, in this case, the Schrodinger equation is the free particle equation. The Aharonov–Bohm effect is a topological effect where the role of the potentials $A_\mu$ (vs electric/magnetic fields) in the creation of a phase difference for two different paths of electrons, is crucial. – Trimok Aug 09 '14 at 10:50
  • No, in the schrodinger equation, you have $A_\mu$ which you know is nonzero. – Jiang-min Zhang Aug 09 '14 at 11:50
  • If you take a constant magnetic field, you may choose the Coulomb gauge, and you may express $\vec A$ as a function of $\vec B$, $\vec A = -\frac{1}{2} \vec r \wedge \vec B$, so finally there is only the magnetic field in the Schrodinger equation, see for instance the formula $(13)$ page $7$ of this paper – Trimok Aug 09 '14 at 12:12
  • Essentially a duplicate of this Phys.SE post and links therein. – Qmechanic Aug 09 '14 at 13:10

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