Timeline for Is commutation relation $[\hat x, \hat p]= i \hbar$ or momentum operator $\hat p = -i \hbar \nabla$ an axiom of QM?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2021 at 19:21 | comment | added | Noiralef | @AlexGower The fact that position and momentum operator are (up to unitary equivalence) uniquely determined by the canonical commutation relations is called the Stone-von Neumann theorem. | |
| Oct 12, 2021 at 13:25 | vote | accept | Alex Gower | ||
| Oct 12, 2021 at 13:12 | comment | added | don't train ai on me | Agreed! At least not in a logical sense. The only argument you can make is pedagogically but that is physics pedagogy and not physics itself. | |
| Oct 12, 2021 at 12:53 | comment | added | Alex Gower | So ultimately, you can equivalently choose to fix the form of $\hat p$ or the cannonical commutation relation, and neither is necessarily a 'better' axiom choice, agreed? | |
| Oct 12, 2021 at 12:53 | comment | added | Alex Gower | Ah I see from one of the comments that there is probably a unitary transformation connecting these alternative forms. | |
| Oct 12, 2021 at 12:48 | comment | added | Alex Gower | This could be obvious, but are there therefore no alternative forms of $\hat p$ that could satisfy the commutation relation? | |
| Oct 12, 2021 at 12:17 | history | answered | don't train ai on me | CC BY-SA 4.0 |