Timeline for A question about the equation $\frac{1}{2}\otimes\frac{1}{2}=1\oplus0$
Current License: CC BY-SA 4.0
16 events
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| Sep 11, 2020 at 1:09 | comment | added | don't train ai on me | Haha. Whoops. My humor was a fail. I'll leave my post up for the first, non-humor part of it. Yes, that's true, $0 \neq 1$. | |
| Sep 10, 2020 at 22:57 | comment | added | ZR- | @Frobenius Thanks for the tip:) | |
| Sep 10, 2020 at 22:44 | vote | accept | ZR- | ||
| Sep 10, 2020 at 21:37 | comment | added | G. Smith | @doublefelix If only we could just remove the circles on the plus signs, everything would be obvious! No, it wouldn’t. It would become $\frac12\times\frac12=1+0$, which is nonsense. It would be obvious as arithmetic if we wrote it in terms the dimensions $2s+1$ of the representations, $2 \times 2=3+1$, instead of in terms of the quantum numbers $s$. | |
| Sep 10, 2020 at 20:41 | answer | added | CR Drost | timeline score: 0 | |
| Sep 10, 2020 at 20:41 | comment | added | ZR- | Thanks!! That helps:) | |
| Sep 10, 2020 at 20:35 | answer | added | Ivan Burbano | timeline score: 1 | |
| Sep 10, 2020 at 20:26 | comment | added | don't train ai on me | Hey Zhengrong, those numbers are the maximal spin of each of the respective particles. For example when we say that the electron has spin 1/2, we really mean its MAXIMAL spin is 1/2. However the actual spin can take values of 1/2 or -1/2. It's just a way of naming things that is at times misleading. Not sure if that's your whole question though.. there is more to know on the meaning of that equation. If only we could just remove the circles on the plus signs, everything would be obvious! ;) | |
| Sep 10, 2020 at 20:21 | history | edited | ZR- | CC BY-SA 4.0 |
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| Sep 10, 2020 at 20:16 | comment | added | ZR- | Thanks for the comment! I do understand the 4 by 4 matrix, but I'm not quite sure what the 3x3 matrix block means, and if '0' and '1' stands for the two spin systems, why there's no '-1' on the right-hand side (if two particles both spin down). | |
| Sep 10, 2020 at 19:51 | comment | added | Cosmas Zachos | Do you understand this is the tensor product of a pair of 2x2 matrices into a 4x4 matrix which reduces to a 3x3 matrix block (triplet) and a singlet ("1") block? | |
| Sep 10, 2020 at 19:49 | comment | added | ZR- | Thanks!! I've seen that page but I'm still a bit confused with what each of the blocks on the right-hand side means. | |
| Sep 10, 2020 at 19:46 | comment | added | Qmechanic♦ | Related: physics.stackexchange.com/q/534887/2451 | |
| Sep 10, 2020 at 19:45 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Sep 10, 2020 at 19:44 | history | edited | ZR- | CC BY-SA 4.0 |
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| Sep 10, 2020 at 19:32 | history | asked | ZR- | CC BY-SA 4.0 |