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ThreeJSymbol

ThreeJSymbol
gives the values of the Wigner 3- symbol.
  • The 3- symbols vanish except when and the satisfy a triangle inequality.
  • The parameters of ThreeJSymbol can be integers, half-integers or symbolic expressions.
  • The Clebsch-Gordan coefficients and 3- symbols in Mathematica satisfy the relation .
Use symbolic arguments to obtain exact symbolic answers:
In[1]:=
Click for copyable input
Out[1]=
 
Use symbolic arguments to obtain exact symbolic answers:
In[1]:=
Click for copyable input
Out[1]=
ThreeJSymbol works with integer and half-integer arguments:
TraditionalForm formatting:
Plot 3- symbol coefficients as a function of and :
Apply angular momentum operators to spherical harmonics:
Evaluate Gaunt coefficients:
Evaluate an explicit triple integral of spherical harmonics:
Evaluate the completely symbolic case of ThreeJSymbol:
Demonstrate -sum orthogonality:
Convert to a Regge R symbol:
Check the symmetry of the Regge R symbol:
Compare with sum definition:
A message is issued and the result 0 returned in the case :
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