1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted