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Homework Help: Inner product

  1. Apr 8, 2007 #1
    1. The problem statement, all variables and given/known data

    What s the inner product [tex]<2011|0011>[/tex]

    2. Relevant equations


    3. The attempt at a solution

    I'm not sure how to exactly solve this question. The first thing that came to my mind was the Clebsch-Gordan equation, since that's what it looks like, but then I saw that it doesnt really make any sense because of this:



    I'm guessing the inner product is zero, but i'm not sure how to show this.

    maybe because since m=0, m_1=1 and m_2=1 wouldnt make sense? not too sure, any help would be appreciated.

  2. jcsd
  3. Apr 8, 2007 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Are you sure that your labels are ordered correctly?

    Yes, it's a CG question, but here the result is trivially zero. In pricniple, you would have to look up a table and write the state [itex] | l_{total} =0, m_{l,total} =0, l_1 =1, l_2=1> [/itex] in terms of the [itex] |l_1,l_2,m_{l,1} m_{l,2}>[/itex] states.

    But if your labels are ordered correctly and l_total = 0 and l_1 = 2 and l_2=0 then the result is trivially zero since adding 2 and 0 only gives a total l equal to 2 (and the m quantum numbers don't match either. if m_1=1 and m_2 =1, then m_total must be 2).

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