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Expectation values of spin operators in changing magnetic field

  1. Dec 25, 2012 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=54252&stc=1&d=1356455629.jpg


    2. Relevant equations



    3. The attempt at a solution
    I have totally no idea how to solve this question. But I find it somehow similar to the Larmor precession problem. Therefore I try to solve my problem by referring to that.
    Are there any mistakes if I do it like this?

    p.s. since the matrix elements are quite complicated, in order to save time, I use "c" to stand for cosine, "e" to stand for exponential that repeat over and over again.
    attachment.php?attachmentid=54253&stc=1&d=1356455634.jpg
     

    Attached Files:

  2. jcsd
  3. Dec 26, 2012 #2

    TSny

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    It looks like you're taking the spin state of the particle at time t = 0 to be proportional to ##\left(\begin{array}{c}1\\0\end{array}\right)##. That would correspond to spin up along the z-axis. But at t = 0 the spin state is an eigenstate of the Hamiltonian H for a magnetic field in the direction specified by ##\theta## and ##\phi##. In particular, it's the state that corresponds to "spin up" along the ##\theta##, ##\phi## direction (or, positive energy eigenvalue for H).
     
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