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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Specific values > Specialized values > Fixed j1, j2, m1, m2





http://functions.wolfram.com/07.38.03.0005.01









  


  










Input Form





ClebschGordan[{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 1] + Subscript[j, 2] - 2, Subscript[m, 1] + Subscript[m, 2]}] == ((Sqrt[Subscript[j, 1]] Sqrt[Subscript[j, 2]] Sqrt[2 Subscript[j, 1] - 1] Sqrt[2 Subscript[j, 2] - 1])/ (Sqrt[Subscript[j, 1] + Subscript[j, 2] - 1] Sqrt[2 Subscript[j, 1] + 2 Subscript[j, 2] - 1])) ((Sqrt[(Subscript[j, 1] - Subscript[m, 1])!] Sqrt[(Subscript[j, 1] + Subscript[m, 1])!] Sqrt[(Subscript[j, 2] - Subscript[m, 2])!] Sqrt[(Subscript[j, 2] + Subscript[m, 2])!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] - Subscript[m, 1] - Subscript[m, 2] - 2)!] Sqrt[(Subscript[j, 1] + Subscript[j, 2] + Subscript[m, 1] + Subscript[m, 2] - 2)!])/(Sqrt[(2 Subscript[j, 1])!] Sqrt[(2 Subscript[j, 2])!] Sqrt[(2 Subscript[j, 1] + 2 Subscript[j, 2] - 4)!])) (((2 Subscript[j, 1] - 2)! (2 Subscript[j, 2] - 2)!)/ ((Subscript[j, 1] - Subscript[m, 1])! (Subscript[j, 1] + Subscript[m, 1] - 2)! (Subscript[j, 2] + Subscript[m, 2])! (Subscript[j, 2] - Subscript[m, 2] - 2)!) - (2 (2 Subscript[j, 1] - 2)! (2 Subscript[j, 2] - 2)!)/ ((Subscript[j, 1] - Subscript[m, 1] - 1)! (Subscript[j, 1] + Subscript[m, 1] - 1)! (Subscript[j, 2] + Subscript[m, 2] - 1)! (Subscript[j, 2] - Subscript[m, 2] - 1)!) + ((2 Subscript[j, 1] - 2)! (2 Subscript[j, 2] - 2)!)/ ((Subscript[j, 1] - Subscript[m, 1] - 2)! (Subscript[j, 1] + Subscript[m, 1])! (Subscript[j, 2] + Subscript[m, 2] - 2)! (Subscript[j, 2] - Subscript[m, 2])!)) /; \[ScriptCapitalP]\[ScriptH]\[ScriptY]\[ScriptS]\[ScriptI]\[ScriptC]\ \[ScriptA]\[ScriptL]\[ScriptCapitalQ][{Subscript[j, 1], Subscript[m, 1]}, {Subscript[j, 2], Subscript[m, 2]}, {Subscript[j, 1] + Subscript[j, 2] - 2, Subscript[m, 1] + Subscript[m, 2]}]










Standard Form





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MathML Form







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





2001-10-29