Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Angular momentum states

  1. Feb 27, 2014 #1
    When we add the angular momenta of two particles, J1 and J2, we get that the resulting total angular momenta is in the range
    |J1-J2| < J < J1+J2

    but according to the Clebsh-Gordan table some coefficients are zero. Does it mean that not all combinations between |J1-J2| and J1+J2 are possible?
  2. jcsd
  3. Feb 27, 2014 #2
    No, they are all possible. The Clebsh-Gordan table also takes the components (the m's) into consideration.
  4. Feb 27, 2014 #3
    ok, but for a given m - some of them might not be possible
  5. Feb 27, 2014 #4


    User Avatar
    Science Advisor

    It's due to symmetry. For example, rotate through 180 degrees, turning z → -z. This reverses the sign of each m value. There's an identity

    (j1 -m1 j2 -m2|j3 -m3) = (-1)j1 + j2 + j3 (j1 m1 j2 m2|j3 m3)

    So in particular for m1 = m2 = m3 = 0 the Clebsch-Gordan coeffiicent will vanish if j1 + j2 + j3 is odd.
  6. Feb 27, 2014 #5
    That's correct
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook