# 3j symbols problem

1. Nov 6, 2011

### dingo_d

1. The problem statement, all variables and given/known data
Show that the state:

$|\Psi\rangle=\sum\limits_{m_1\ m_2\ m_3}\begin{pmatrix} j_1 & j_2 & j_3 \\ m_1 & m_2 & m_3 \\ \end{pmatrix}|j_1\ m_1\rangle |j_2\ m_2\rangle |j_3\ m_3\rangle$

has the total angular momentum equal to zero.

2. Relevant equations

There are bunch of formulas for Clebsch - Gordan coefficients and Wigner 3j symbols, but that can be found everywhere.

3. The attempt at a solution

I have absolutely no idea how to start this one :\

I could write explicitly the 3j symbols, but then what?

EDIT: I found in Landau & Lifgarbagez, that this is what you should get for system of 3 particles with total angular momentum 0, but how do I prove that? They left that part out...

Last edited: Nov 6, 2011