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A eigenstate of addition of angular momenta

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data
    Find eigenstates(of[tex]L_z[/tex]) [tex]|2~0\rangle[/tex]

    2. Relevant equations

    3. The attempt at a solution
    [tex]|l=3~m=3\rangle=|l_1=2~m_1=2\rangle|l_2=1~m_2=1 \rangle[/tex]. I do [tex]L_-=L_{1-}+L_{2-}[/tex] 3times.
    So I get [tex]|3~0\rangle[/tex]= (omit)
    Then How can I find [tex]2~0\rangle[/tex]?
    I know that [tex]2~0\rangle[/tex] is orthogonal to [tex]|3~0\rangle[/tex]. But I don't know how to use that property to derive a result.
    Please give me an answer.
  2. jcsd
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