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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Summation > Finite summation > Involving three Clebsch Gordan coefficients





http://functions.wolfram.com/07.38.23.0022.01









  


  








Input Form





Sum[(-1)^(Subscript[j, 1] - Subscript[m, 1]) ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 3], -Subscript[m, 3]}, {Subscript[j, 2], Subscript[m, 2]}] ClebschGordan[{Subscript[j, 6], Subscript[m, 6]}, {Subscript[j, 2], -Subscript[m, 2]}, {Subscript[j, 4], Subscript[m, 4]}] ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 6], Subscript[m, 6]}], {Subscript[m, 1], -Subscript[j, 1], Subscript[j, 1]}, {Subscript[m, 2], -Subscript[j, 2], Subscript[j, 2]}, {Subscript[m, 6], -Subscript[j, 6], Subscript[j, 6]}] == (-1)^(Subscript[j, 2] + Subscript[j, 3] + Subscript[j, 5] + Subscript[j, 6]) Sqrt[2 Subscript[j, 2] + 1] Sqrt[2 Subscript[j, 6] + 1] ClebschGordan[{Subscript[j, 3], Subscript[m, 3]}, {Subscript[j, 5], Subscript[m, 5]}, {Subscript[j, 4], Subscript[m, 4]}] SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}]








Standard Form





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MathML Form







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<cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </list> </apply> <apply> <ci> SixJSymbol </ci> <list> <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> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 6 </cn> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "1"], "=", RowBox[List["-", SubscriptBox["j", "1"]]]]], SubscriptBox["j", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "2"], "=", RowBox[List["-", SubscriptBox["j", "2"]]]]], SubscriptBox["j", "2"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["m_", "6"], "=", RowBox[List["-", SubscriptBox["j", "6"]]]]], SubscriptBox["j", "6"]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["m_", "1"]]]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", RowBox[List["-", SubscriptBox["m_", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]]]], "]"]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m_", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", RowBox[List["-", SubscriptBox["m_", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["m_", "4"]]], "}"]]]], "]"]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["m_", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "6"], ",", SubscriptBox["m_", "6"]]], "}"]]]], "]"]]]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["j", "3"], "+", SubscriptBox["j", "5"], "+", SubscriptBox["j", "6"]]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "2"]]], "+", "1"]]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", SubscriptBox["j", "6"]]], "+", "1"]]], " ", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "3"], ",", SubscriptBox["mm", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "5"], ",", SubscriptBox["mm", "5"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["mm", "4"]]], "}"]]]], "]"]], " ", RowBox[List["SixJSymbol", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["j", "2"], ",", SubscriptBox["j", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "4"], ",", SubscriptBox["j", "5"], ",", SubscriptBox["j", "6"]]], "}"]]]], "]"]]]]]]]]


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





2001-12-21