Review of wigner nj-Symbols

This week I’ve been reviewing the properties of the Wigner nj symbols.

3j-Symbols

Relation to Clebsh-Gordan coefficients:

6wigner1

 

Compatibility criteria

6wignerabcvanishes if the following are not true:

6wigner2

Symmetries

6wigner3

6j-Symbols
Definition in terms of 3j’s

6wigner4

Symmetries

6wigner5

Compatibility

6wigner6,

unless the triangle inequalities hold for {a,b;,c};    {a,e;,f}, {d,b,f}and {d,e,c}

 

Orthogonality

6wigner7

 

9j-Symbols

Definition by 3j’s

6wigner8

Definition by 6j’s

6wigner9

Symmetries

6wigner10

 

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