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Spin expectation value of singlet state from two axes

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data

    W0xJo.jpg

    2. Relevant equations

    955051058cb93d9219b5d784953f155a.png

    c8ef092164e2dae009fe706c21e24672.png

    51f1b89d374b15ab20a813d1ed3cc690.png

    ba83b5f185b2ad5ddd006c74328b6034.png

    7154c9d3b5d2aa4193e3a6c9e85aff80.png

    3. The attempt at a solution

    I am just trying to figure out how to start the problem. Any help would be greatly appreciated.
     
    Last edited by a moderator: Apr 17, 2017
  2. jcsd
  3. Dec 4, 2012 #2
    Start by writing S1 and S2 in terms of the pauli matrices.
     
  4. Dec 4, 2012 #3
    Would S1=Sz and S2 have cos(θ) instead of 1's in the matrix?
     
  5. Dec 4, 2012 #4
    Yes, but you need to be careful about the sign, whether it is cos(θ) or -cos(θ), since the question says -"makes an angle θ down with the z axis".
     
  6. Dec 4, 2012 #5
    Ok, but what does the question mean by picking a single basis to work in? I just don't know what the question is saying.
     
    Last edited: Dec 4, 2012
  7. Dec 6, 2012 #6
    I believe they are trying to tell you to have both S_1 and S_2 in the same basis, i.e, either choose S_1 to lie along z-axis and S_2 to lie theta away from it, or choose S_2 to lie along z-axis and S_1 to lie -theta away from it.

    Since they already chose the first of these options, the hint is redundant (as the author say so themselves!).
     
  8. Dec 6, 2012 #7
    may be it will be clear if I show some solution,
    Using the notation of question and I use + for up and - for down,

    <00|S1S2|00>=-h-/2.h-/2 cosθ.(1/2)(<+-|+->+<-+|-+>),other two terms in brackets which you get are zero because of orthogonality condition.(The extra minus sign in front is just because cos(1800-θ)=-cosθ) and you will get this
    =-h-2/4.cosθ(because <+-|+->=1 and similarly for other)
    edit:I hope this post will not be deleted like some of my previous ones.
     
  9. Dec 6, 2012 #8
    Thank you andrien, your answer was clear and to the point. I don't know why your other posts would have been deleted but this one won't be.
     
  10. Dec 7, 2012 #9
    it is just because I can not do anyone's homework in this section.I have already gotten infraction for this.But you saw it,so cheers!
     
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