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Problem in constructing Matrix representation in |↑↓> basis

  1. Dec 13, 2011 #1
    If I want to derive the matrix representation for operator Q in the |S1=1/2 ,m1> |S2=1/2 ,m2 > basis, where |Si,mi> are common eigenstates of S2 , Si,z for the ith particle.

    And I do it in this way:
    <↑↑|Q|↑↑> <↑↑|Q|↑↓> <↑↓|Q|↓↑> <↑↑|Q|↓↓>
    <↑↓|Q|↑↑> <↑↓|Q|↑↓> <↑↓|Q|↓↑> <↑↓|Q|↓↓>
    .... .... .... ....
    .... .... .... ....

    |↑↑>=|S1=1/2 ,m1=+1/2> |S2=1/2 ,m2=+1/2 >
    Is it correct?
  2. jcsd
  3. Dec 13, 2011 #2
    can anyone help?
  4. Dec 13, 2011 #3


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    Let's see...the ij component (row i, column j) in the basis [itex]\{e_i\}[/itex] is [itex]Q_{ij}=(Qe_j)_i=\langle e_i,Qe_j\rangle[/itex]. In bra-ket notation, [itex]Q_{ij}=\langle i|Q|j\rangle[/itex]. So everything on your first row should have the same "bra", but one of them is different from the other three. I suspect it's just a typo, since the rest of it looks fine.
  5. Dec 13, 2011 #4
    oh,ya, you are right, it's just a typo. Thanks for teaching:smile:
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