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ClebschGordan




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Primary definition





http://functions.wolfram.com/07.38.02.0001.01









  


  








Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}] == KroneckerDelta[m, Subscript[m, 1] + Subscript[m, 2]] ((Sqrt[1 + 2 j] Sqrt[(j + Subscript[j, 1] - Subscript[j, 2])!] Sqrt[(j - Subscript[j, 1] + Subscript[j, 2])!] Sqrt[(j - m)!] Sqrt[(j + m)!] Sqrt[(Subscript[j, 1] + Subscript[m, 1])!] Sqrt[(Subscript[j, 2] - Subscript[m, 2])!])/ (Sqrt[(Subscript[j, 1] + Subscript[j, 2] - j)!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] + j + 1)!] Sqrt[(Subscript[j, 1] - Subscript[m, 1])!] Sqrt[(Subscript[j, 2] + Subscript[m, 2])!])) HypergeometricPFQRegularized[{j - Subscript[j, 1] - Subscript[j, 2], -Subscript[j, 1] + Subscript[m, 1], -Subscript[j, 2] - Subscript[m, 2]}, {1 + j - Subscript[j, 2] + Subscript[m, 1], 1 + j - Subscript[j, 1] - Subscript[m, 2]}, 1] /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\ \[ScriptI]\[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ][ {Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {j, m}]








Standard Form





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MathML Form







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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> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "m_"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List["m", ",", RowBox[List[SubscriptBox["mm", "1"], "+", SubscriptBox["mm", "2"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", RowBox[List["2", " ", "j"]]]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["j", "+", SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["j", "-", SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["j", "-", "m"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["j", "+", "m"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["mm", "1"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "-", SubscriptBox["mm", "2"]]], ")"]], "!"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["j", "-", SubscriptBox["j", "1"], "-", SubscriptBox["j", "2"]]], ",", RowBox[List[RowBox[List["-", SubscriptBox["j", "1"]]], "+", SubscriptBox["mm", "1"]]], ",", RowBox[List[RowBox[List["-", SubscriptBox["j", "2"]]], "-", SubscriptBox["mm", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "j", "-", SubscriptBox["j", "2"], "+", SubscriptBox["mm", "1"]]], ",", RowBox[List["1", "+", "j", "-", SubscriptBox["j", "1"], "-", SubscriptBox["mm", "2"]]]]], "}"]], ",", "1"]], "]"]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "-", "j"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "+", SubscriptBox["j", "2"], "+", "j", "+", "1"]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "1"], "-", SubscriptBox["mm", "1"]]], ")"]], "!"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["j", "2"], "+", SubscriptBox["mm", "2"]]], ")"]], "!"]]]]]], "/;", RowBox[List["\[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\[ScriptA]\[ScriptL]\[ScriptCapitalQ]", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["mm", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["mm", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "m"]], "}"]]]], "]"]]]]]]]]


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





2001-10-29