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Homework Help: Sakurai chapter 3, Problem 1.

  1. Feb 12, 2014 #1
    hello guys

    Suppose an electron is in the spin state alpha=(a,b). if s_y is measured, what is the probability of result h/2 ?

    s_y eigenvector for +h/2 is |y+>=1/sqrt(2) (1,i)) so the probabilty is (<y+|alpha>)^2 . but in the solution i attached , the solution is different ! i'm confused !

    thank you for your help

    Attached Files:

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  2. jcsd
  3. Feb 12, 2014 #2
    Don't bother, your solution is correct.
  4. Feb 12, 2014 #3
    so the solution is incorrect ?
  5. Feb 12, 2014 #4
    well there's certainly something wrong when you measure a probability in terms of [itex]\hbar[/itex]2...
  6. Feb 12, 2014 #5


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    Yes, the solution is incorrect. Whoever wrote it made the common mistake of conflating making a measurement with applying the associated operator. In other words, the "solution" calculates ##\langle +_y \lvert \hat{S}_y \rvert \alpha,\beta\rangle## for the probability amplitude while you correctly calculated ##\langle +_y \vert \alpha,\beta\rangle##.
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