Clebsch–Gordan coefficient
coefficients in angular momentum eigenstates of quantum systems
| rdfs:label |
"Clebsch–Gordan coefficient"@en
|
|
skos:alt |
"Clebsch-Gordan coefficient"@en
|
| schema:description |
"coefficients in angular momentum eigenstates of quantum systems"@en
|
|
schema:date |
"2026-08-10T00:07:54+00:00"^^xsd:dateTime |
| schema:version | 2529407377 |
| wikibase:identifiers | 7 |
| wikibase:sitelinks | 20 |
| wikibase:statements | 16 |
| p:P10283 | wd:statement/Q898619-3AF19A0D-512C-4FA3-BD58-DE338627511A |
| p:P10565 | wd:statement/Q898619-BB9020FC-17BE-4B7D-99C1-2CAB71551E9A |
| p:P138 | wd:statement/Q898619-39e61bbc-418b-13f6-c7bb-e57b426d5041 |
| wd:statement/Q898619-47ed9051-47c4-35d8-2342-ca50aada0cee | |
| p:P14541 | wd:statement/Q898619-3017D25A-9BA2-4ABC-A44B-C9639D6B9EEE |
| p:P2534 | wd:statement/Q898619-54B24E69-E23C-4021-8EB6-6E61B0121C10 |
| p:P279 | wd:statement/Q898619-4a5a0310-4515-3b34-6a9e-808272a80270 |
| p:P2812 | wd:statement/Q898619-dd141e70-4fb9-afd5-9bf1-79382f89aadc |
| p:P31 | wd:statement/Q898619-3ec351ff-4463-a78e-eba9-14f80e831d77 |
| p:P5064 | wd:statement/Q898619-8f67bb20-4a9b-7646-7022-cbae1bbfc09c |
| p:P6104 | wd:statement/Q898619-F51899E7-9BF2-4372-A3D8-BF62FB7D9108 |
| p:P6366 | wd:statement/Q898619-E4ED1778-45CD-45F5-8FF3-CA9F266FDCE4 |
| p:P646 | wd:statement/Q898619-3EE60AB9-0B4F-4107-ABC2-DFE114E341FD |
| p:P7235 | wd:statement/Q898619-3e54354b-49c4-877b-c371-877a6c15db52 |
| wd:statement/Q898619-4d2d0af3-40ae-3152-99ce-c874b8cf452d | |
| wd:statement/Q898619-68b480e7-4849-7c34-6c5e-a5a84790e728 | |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C23503194" |
| wdt:P10565 | "215494" |
| wdt:P138 | Alfred Clebsch |
| Paul Gordan | |
| wdt:P14541 | "37Ert8" |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">⟨</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>;</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">∣</mo><mi>J</mi><mo>,</mo><mi>M</mi><mo stretchy="false">⟩</mo><mo stretchy="false">=</mo><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>M</mi><mo>,</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mi>J</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">+</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">−</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><mi>J</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">+</mo><mi>J</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">!</mo></mrow></mrow></mfrac></mrow></msqrt></mrow><mo stretchy="false">×</mo><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">+</mo><mi>M</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">−</mo><mi>M</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">!</mo></mrow></msqrt></mrow><mo stretchy="false">×</mo><munder><mo stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></munder><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mo stretchy="false">−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><mi>J</mi><mo stretchy="false">−</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">−</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">−</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">+</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo></mrow></mrow></mfrac></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P279 | special function |
| wdt:P2812 | "Clebsch-GordanCoefficient" |
| wdt:P31 | mathematical concept |
| wdt:P5064 | "Clebsch-GordanCoefficient" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "23503194" |
| wdt:P646 | "/m/043r3j" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">!</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">⟨</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>;</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">∣</mo><mi>J</mi><mo>,</mo><mi>M</mi><mo stretchy="false">⟩</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>M</mi><mo>,</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">+</mo><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
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