Timeline for Why can we say that the cross product of $\hat{x}$ and $\hat{p}$ will give the quantum operator $\hat{L}$?
Current License: CC BY-SA 4.0
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| Nov 7, 2022 at 3:07 | vote | accept | Dutonic | ||
| Nov 7, 2022 at 1:56 | answer | added | ACuriousMind♦ | timeline score: 9 | |
| Nov 7, 2022 at 1:40 | answer | added | ZeroTheHero | timeline score: 2 | |
| Nov 7, 2022 at 1:36 | history | edited | Buzz♦ | CC BY-SA 4.0 |
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| Nov 7, 2022 at 1:35 | answer | added | Buzz♦ | timeline score: 6 | |
| Nov 7, 2022 at 0:55 | history | edited | Dutonic | CC BY-SA 4.0 |
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| Nov 7, 2022 at 0:42 | history | edited | Qmechanic♦ |
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| Nov 7, 2022 at 0:35 | comment | added | d_b | @Dutonic It's hard to imagine what a proof would be. One argument that you could make is that the angular momentum is the symmetry charge associated with rotational symmetry, so whatever the angular momentum operator is it should be the generator of rotations. But then the whole idea that symmetry charges generate the corresponding symmetries is really just a postulate that needs to be verified experimentally... like the whole rest of the theoretical apparatus. | |
| Nov 7, 2022 at 0:33 | comment | added | Ghoster | You seem to have the misconception that physical theories can ever be proved. They can’t. | |
| Nov 7, 2022 at 0:33 | answer | added | don't train ai on me | timeline score: -2 | |
| Nov 7, 2022 at 0:16 | comment | added | Dutonic | @Ghoster To clarify, the purpose of this question is to gain an understanding of the theoretical foundations for why we make this assumption. Are we postulating this relationship between quantum operators and their classical counterparts, or is there a proof behind it? I'm perfectly aware of how experimentalists check the accuracy of theories... | |
| Nov 7, 2022 at 0:02 | comment | added | Ghoster | By assuming it and then testing whether theoretical predictions following from that assumption match observation… the same way we become confident in any theoretical idea. | |
| Nov 6, 2022 at 23:55 | comment | added | Dutonic | @basics Obviously L = r x p in classical mechanics. The question is about how we can definitively demonstrate that this definition holds for quantum operators | |
| Nov 6, 2022 at 23:52 | comment | added | basics | it's like the definition of the angular momentum in classical mechanics | |
| Nov 6, 2022 at 23:44 | history | asked | Dutonic | CC BY-SA 4.0 |