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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Identities > Functional identities > Involving three Clebsch Gordan coefficients





http://functions.wolfram.com/07.38.17.0064.01









  


  










Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] == ClebschGordan[{Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 1], Subscript[m, 1]}, {j, m}] Csc[Pi (j - Subscript[j, 1] + Subscript[m, 2])] Sin[Pi (Subscript[j, 2] + Subscript[m, 2])] + (1/Sqrt[1 + j + Subscript[j, 1] - Subscript[m, 2]]) (Sqrt[1 + 2 j] ClebschGordan[{Subscript[j, 2], -j + Subscript[j, 1]}, {(1/2) (j + Subscript[j, 1] + Subscript[m, 2]), (1/2) (j - Subscript[j, 1] + Subscript[m, 1] + m)}, {(1/2) (j + Subscript[j, 1] - Subscript[m, 2]), (1/2) (-j + Subscript[j, 1] + Subscript[m, 1] + m)}] Csc[Pi (j - Subscript[j, 1] + Subscript[m, 2])] Sin[Pi (j - Subscript[j, 1] - Subscript[j, 2])]) /; Re[Subscript[j, 1] + Subscript[j, 2] + j] > -2










Standard Form





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MathML Form







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</mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <ci> j </ci> <ci> m </ci> </list> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <ci> j </ci> <ci> m </ci> </list> </apply> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> csc </ci> <apply> <times /> <pi /> <apply> <plus /> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <ci> j </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> j </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ClebschGordan </ci> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </list> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </list> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <ci> m </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </list> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <real /> <apply> <plus /> <ci> j </ci> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29