# Explanation of 6j Symbols (Tetrahedron)

1. Mar 30, 2012

### Tilde90

Hello all! (I'm new to the forum)
I'd like to ask if you could give me a simple explanation regarding the 6j symbols: I don't understand their formulation in terms of Clebsch-Gordan coefficients with three angular momenta and the related "tetrahedron rule".
Alternatively, could you please suggest me a book to consult?
Thank you very much for your help!

Last edited: Mar 30, 2012
2. Apr 1, 2012

### Bill_K

Tilde90, Angular momentum can be a really complicated subject. As you probably know (or you wouldn't be asking this!) the 6-j symbols are involved in coupling three angular momenta. You can couple j1 and j2 to form j12, then j12 and j3 to form J. Or, you can couple j2 and j3 to form j23, then j23 and j1 to form J. The 6-j symbols describe a unitary transformation between the two ways of doing things. And naturally they involve six angular momenta, j1, j2, j3, j12, j23 and J.

A book reference, including a discussion of the tetrahedron diagram, is the monograph, "Angular Momentum in Quantum Mechanics" by A.R. Edmonds, section 6.1.

3. Apr 1, 2012

Staff Emeritus
I would second the recommendation for Edmonds.

4. Apr 3, 2012