Timeline for Do functions defined on a torus have to be periodic?
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12 events
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| Sep 20, 2023 at 13:51 | comment | added | TheQuantumMan | @J.Murray Sorry for being a bit late to the party here, but if you take a look to my recent question: physics.stackexchange.com/questions/777579/… you'll see that your comment is directly relevant. If we impose periodic BCs without a "phase shift", the wavefunction with an Aharonov-Bohm phase fails to satisfy the perioic BCs, except if we quantise the magnetic flux, which seems dissatisfying to me, since the magnetic flux is an external parameter. So, the boundary conditions are indeed the ones you mentioned? | |
| Sep 18, 2022 at 15:38 | comment | added | Albatross | @lisyarus Not a shift in the wavefunction $\psi \mapsto e^{ikx}\psi$, but rather a quasi-periodic boundary condition $\psi(1)=e^{i\theta} \psi(0)$. This is indeed observable; this is what happens e.g. to a particle on a ring which is threaded by some non-zero magnetic flux. The phase accumulated by going around the ring once is the Aharanov-Bohm phase. | |
| Sep 18, 2022 at 15:34 | vote | accept | Kleber | ||
| Sep 18, 2022 at 15:29 | answer | added | Albatross | timeline score: 2 | |
| Sep 18, 2022 at 15:23 | comment | added | Raad Shaikh | @lisyarus I must admit I'm not sure of the details, I just read this in the 'Quantization' section in here: en.m.wikipedia.org/wiki/Angular_momentum_operator | |
| Sep 18, 2022 at 15:12 | comment | added | lisyarus | @RaadShaikh Wouldn't a phase shift mean a change in momentum, thus be an observable effect? I agree with you on a global constant phase shift, though, since wavefunctions are really elements of the projectivisation of the Hilbert space, not the space itself. | |
| Sep 18, 2022 at 15:04 | history | edited | Kleber | CC BY-SA 4.0 | deleted 9 characters in body |
| Sep 18, 2022 at 13:07 | comment | added | Raad Shaikh | A function is by definition single-valued, so indeed a function defined on a torus must take the same value at equivalent points. It is worth noting, however, that some authors argue that the wavefunction is not directly observable and hence need not be single-valued - it can acquire a phase shift upon making a round trip through space (as long as its squared amplitude is the same). | |
| Sep 18, 2022 at 10:46 | history | edited | Kleber | CC BY-SA 4.0 | edited title |
| Sep 18, 2022 at 10:06 | history | edited | Kleber | CC BY-SA 4.0 | added 29 characters in body |
| Sep 18, 2022 at 9:41 | history | edited | Kleber | CC BY-SA 4.0 | added 7 characters in body |
| Sep 18, 2022 at 9:36 | history | asked | Kleber | CC BY-SA 4.0 |