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Homework Help: 3j symbols problem

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that the state:

    [itex]|\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[/itex]

    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
  2. jcsd
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