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ClebschGordan

ClebschGordan
gives the Clebsch-Gordan coefficient for the decomposition of in terms of .
  • The Clebsch-Gordan coefficients vanish except when and the satisfy a triangle inequality.
  • The parameters of ClebschGordan can be integers, half-integers, or symbolic expressions.
  • Mathematica uses the standard conventions of Edmonds for the phase of the Clebsch-Gordan coefficients.
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]=
ClebschGordan works with integer and half-integer arguments:
For symbolic input ClebschGordan evaluates to ThreeJSymbol:
Plot Clebsch-Gordan coefficients as a function of and :
Decompose a spherical harmonic into a sum of products of two spherical harmonics:
Apply angular momentum operators to spherical harmonics:
Evaluate the completely symbolic case of ClebschGordan:
Demonstrate -sum orthogonality:
A message is issued and the result of 0 is returned when :
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