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ClebschGordan






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ClebschGordan[{j1,m1},{j2,m2},{j,m}] > Summation > Finite summation > Involving two Clebsch Gordan coefficients and one 6j symbol





http://functions.wolfram.com/07.38.23.0035.01









  


  










Input Form





Sum[(-1)^(c + d + f) Sqrt[2 c + 1] Sqrt[2 e + 1] ClebschGordan[{e, \[Epsilon]}, {a, \[Alpha]}, {f, \[CurlyPhi]}] ClebschGordan[{d, \[Delta]}, {c, \[Gamma]}, {f, \[CurlyPhi]}] SixJSymbol[{b, a, c}, {f, d, e}], {f, Max[Abs[a - e], Abs[c - d]], Min[a + e, c + d]}, {\[CurlyPhi], -f, f}] == ClebschGordan[{a, \[Alpha]}, {b, \[Beta]}, {c, \[Gamma]}] ClebschGordan[{d, \[Delta]}, {b, \[Beta]}, {e, \[Epsilon]}]










Standard Form





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MathML Form







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</ci> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </lowlimit> <uplimit> <ci> f </ci> </uplimit> <apply> <sum /> <bvar> <ci> f </ci> </bvar> <lowlimit> <apply> <max /> <apply> <abs /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> </apply> </apply> <apply> <abs /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> </apply> </apply> </lowlimit> <uplimit> <apply> <min /> <apply> <plus /> <ci> a </ci> <ci> e </ci> </apply> <apply> <plus /> <ci> c </ci> <ci> d </ci> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> c </ci> <ci> d </ci> <ci> f </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> e </ci> <ci> &#1013; </ci> </list> <list> <ci> a </ci> <ci> &#945; </ci> </list> <list> <ci> f </ci> <ci> &#966; </ci> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> d </ci> <ci> &#948; </ci> </list> <list> <ci> c </ci> <ci> &#947; </ci> </list> <list> <ci> f </ci> <ci> &#966; </ci> </list> </apply> <apply> <ci> SixJSymbol </ci> <list> <ci> b </ci> <ci> a </ci> <ci> c </ci> </list> <list> <ci> f </ci> <ci> d </ci> <ci> e </ci> </list> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> ClebschGordan </ci> <list> <ci> a </ci> <ci> &#945; </ci> </list> <list> <ci> b </ci> <ci> &#946; </ci> </list> <list> <ci> c </ci> <ci> &#947; </ci> </list> </apply> <apply> <ci> ClebschGordan </ci> <list> <ci> d </ci> <ci> &#948; </ci> </list> <list> <ci> b </ci> <ci> &#946; </ci> </list> <list> <ci> e </ci> <ci> &#1013; </ci> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-12-21





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