# Homework Help: Clebsch-Gordan Coefficients for three spin-1 particles?

1. Apr 29, 2013

### dipole

I'm doing a problem where I need to know the coefficients to change from the
$\vec{J} = \vec{J}_1 + \vec{J}_2 + \vec{J}_3$ to the {$\vec{J}_1, \vec{J}_2, \vec{J}_3$} for three spin-1 particles, but I'm having trouble finding a table or reference for this... surely every time someone needs to write such a wave function they don't do all the algebra by hand, so where can I find a table to do this?

2. Apr 29, 2013

### vela

Staff Emeritus
You combine the angular momenta two at a time.

3. Apr 29, 2013

### dipole

This doesn't really help me...

For my situation, suppose I want to find all the states with $m = 2$. Well, there are three possibilities:

$\mid j = 3, m =2 \rangle$

and then two distinct states with $\mid j = 2, m = 2 \rangle$ which correspond to a
symmetric and anti-symmetric state, presumably. How can I construct these by just coupling $j_{12}$ with $j_3$ (where $j_{12}$ is the coupled-states of $j_1$ and $j_2$)? How do I even start and how do I know which linear combinations to couple to which? It's very confusing. :(

4. Apr 30, 2013

### vela

Staff Emeritus
Well, give it a shot. There's no shortcut method if that's what you're looking for.