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Clebsch-Gordan Coefficients for three spin-1 particles?

  1. Apr 29, 2013 #1
    I'm doing a problem where I need to know the coefficients to change from the
    [itex] \vec{J} = \vec{J}_1 + \vec{J}_2 + \vec{J}_3 [/itex] to the {[itex]\vec{J}_1, \vec{J}_2, \vec{J}_3[/itex]} 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. jcsd
  3. Apr 29, 2013 #2

    vela

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    You combine the angular momenta two at a time.
     
  4. Apr 29, 2013 #3
    This doesn't really help me...

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

    [itex] \mid j = 3, m =2 \rangle [/itex]

    and then two distinct states with [itex] \mid j = 2, m = 2 \rangle [/itex] which correspond to a
    symmetric and anti-symmetric state, presumably. How can I construct these by just coupling [itex] j_{12} [/itex] with [itex] j_3 [/itex] (where [itex] j_{12} [/itex] is the coupled-states of [itex] j_1 [/itex] and [itex] j_2 [/itex])? How do I even start and how do I know which linear combinations to couple to which? It's very confusing. :(
     
  5. Apr 30, 2013 #4

    vela

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