I can only seem to find vague sources explaining Aharonov-Bohm, usually saying things as "the different paths of an electron interfere". I presume this is language borrowed from a Feynman path integral formulation of QM, but I'm not familiar with that yet, so I'd rather see it explained in "ordinary" QM math.(adsbygoogle = window.adsbygoogle || []).push({});

Some sources seem to suggest that the basic consequence of a vector potential is that the phase [itex]S[/itex] of the wavefunction [itex]\psi(\mathbf r,t) = R(\mathbf r,t) e^{iS(\mathbf r,t)}[/itex] gets an extra term, namely the path integral [itex]\int_{\mathbf r_0}^{\mathbf r} \mathbf A(\mathbf r') \cdot \mathrm d \mathbf r'[/itex] (where [itex]\mathbf r_0[/itex] is some arbitrary reference point). Then again, this can't really be true, cause then phase wouldn't be well-defined (since a different path, but also going from r_0 to r, could give a different result). I realize that this last remark is also the key concept in the AB effect, but still, not in the aforementioned way, right? After all, phase shouldn't be ambiguous (except for a 2pi multiple of course). Actually, it's exactly this argument (that different path integrals should give the same phase mod 2pi) that is used to argue flux quantization in a superconducting ring... So why does it not apply more generally?

As you can see, I'm a bit confused. Note that I'm not looking for a vague explanation, I'm looking for something concrete (and well-defined) mathematically. Thank you!

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# Now what is Aharonov-Bohm really?

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