Timeline for Single sum of squares of Clebsch–Gordan coefficients
Current License: CC BY-SA 4.0
16 events
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| Aug 5 at 13:04 | comment | added | eriugena | Assuming this holds nevertheless, do you happen to know (or remember) if the above sum has a similarly nice form for general $j_3$? What I get by using identities for $m_1 = j_1$ is very ugly. | |
| Aug 3 at 4:58 | comment | added | Carlo Beenakker | It’s been a while, I don’t recall having a proof. | |
| Aug 2 at 18:21 | comment | added | eriugena | @CarloBeenakker How do the restrictions you name (which are really the "built-in" conditions vor a non-vanishing CGC, as you say) imply that the sum is independent of $m_1$? | |
| Jul 9, 2023 at 20:57 | comment | added | onamoonlessnight | @CarloBeenakker Thank you, this is exactly what I was looking for. | |
| Jul 9, 2023 at 20:56 | vote | accept | onamoonlessnight | ||
| Jul 9, 2023 at 19:36 | comment | added | LSpice | Re, thanks! | |
| Jul 9, 2023 at 19:36 | comment | added | Carlo Beenakker |
there is not much code to post, actually; the orthogonality relation is Sum[(ClebschGordan[{j1, m1}, {j2, m3 - m1}, {j3, m3}])^2, {j3, Abs[j1 - j2], j1 + j2, 1}, {m3, -j3, j3}] For the evaluation of $J$ I omit the sum over $j_3$.
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| Jul 9, 2023 at 18:22 | comment | added | LSpice | You mention that you used Mathematica. Would you be willing to post the code? (Or a link to a gist, as I believe you have sometimes done.) | |
| Jul 9, 2023 at 17:33 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 16:50 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 16:45 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 16:30 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 16:24 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 15:07 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 14:48 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 9, 2023 at 14:42 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |