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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Identities > Functional identities > Arguments j1, j2, m1, m2 changing by 1





http://functions.wolfram.com/07.38.17.0035.01









  


  










Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2] + 1, Subscript[m, 2]}, {j, m}] == ((Sqrt[Subscript[j, 1] - Subscript[m, 1]] Sqrt[Subscript[j, 1] - Subscript[m, 1] - 1] Sqrt[Subscript[j, 1] + Subscript[j, 2] - j] Sqrt[Subscript[j, 1] + Subscript[j, 2] - j + 1] Sqrt[Subscript[j, 1] + Subscript[j, 2] + j + 1] Sqrt[Subscript[j, 1] + Subscript[j, 2] + j + 2])/ (2 Subscript[j, 1] (2 Subscript[j, 1] + 1) Sqrt[Subscript[j, 2] + Subscript[m, 2]] Sqrt[Subscript[j, 2] + Subscript[m, 2] + 1])) ClebschGordan[{Subscript[j, 1] - 1, Subscript[m, 1] + 1}, {Subscript[j, 2], Subscript[m, 2] - 1}, {j, m}] - ((Sqrt[Subscript[j, 1] - Subscript[m, 1]] Sqrt[Subscript[j, 1] + Subscript[m, 1] + 1] Sqrt[-Subscript[j, 1] + Subscript[j, 2] + j + 1] Sqrt[Subscript[j, 1] - Subscript[j, 2] + j] Sqrt[Subscript[j, 1] + Subscript[j, 2] - j + 1] Sqrt[Subscript[j, 1] + Subscript[j, 2] + j + 2])/ (2 Subscript[j, 1] (Subscript[j, 1] + 1) Sqrt[Subscript[j, 2] + Subscript[m, 2]] Sqrt[Subscript[j, 2] + Subscript[m, 2] + 1])) ClebschGordan[{Subscript[j, 1], Subscript[m, 1] + 1}, {Subscript[j, 2], Subscript[m, 2] - 1}, {j, m}] + ((Sqrt[Subscript[j, 1] + Subscript[m, 1] + 1] Sqrt[Subscript[j, 1] + Subscript[m, 1] + 2] Sqrt[-Subscript[j, 1] + Subscript[j, 2] + j] Sqrt[-Subscript[j, 1] + Subscript[j, 2] + j + 1] Sqrt[Subscript[j, 1] - Subscript[j, 2] + j] Sqrt[Subscript[j, 1] - Subscript[j, 2] + j + 1])/ (2 (Subscript[j, 1] + 1) (2 Subscript[j, 1] + 1) Sqrt[Subscript[j, 2] + Subscript[m, 2]] Sqrt[Subscript[j, 2] + Subscript[m, 2] + 1])) ClebschGordan[{Subscript[j, 1] + 1, Subscript[m, 1] + 1}, {Subscript[j, 2], Subscript[m, 2] - 1}, {j, m}]










Standard Form





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MathML Form







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&#8287; </mtext> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mrow> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mtext> &#8287; </mtext> <mo> &#10072; </mo> <mtext> &#8287; </mtext> <mrow> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mi> j </mi> <mo> &#8290; </mo> <mtext> &#8287; </mtext> <mi> m </mi> </mrow> </mrow> <mo> &#9002; </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[LeftAngleBracket]&quot;, RowBox[List[RowBox[List[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;1&quot;], &quot;+&quot;, &quot;1&quot;]], &quot;\[MediumSpace]&quot;, SubscriptBox[&quot;j&quot;, &quot;2&quot;], &quot;\[MediumSpace]&quot;, RowBox[List[SubscriptBox[&quot;m&quot;, &quot;1&quot;], 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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