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Probability of measuring spin

  1. Dec 27, 2012 #1
    1. The problem statement, all variables and given/known data
    A spin-1 particle is placed in a constatn external B field
    with [itex] B_0 [/itex] in the x direction. the intial spin of the particle
    is spin up in the z direction.
    Take the spin Hamiltonian to be [itex] H=\omega_0 S_x [/itex]
    determine the probability that the particle is in the state |1,-1> at time t.
    3. The attempt at a solution
    Would I start with using the [itex] S_x [/itex] matrix in the z basis and then
    set this equal to spin 1 and then find the eigenvector for this equation and that
    will give me the amplitudes for spin-1, spin-0 and spin minus 1 and these will be amplitudes
    in the x basis then I will just time evovle that intial state.
    So I will have [itex] S_xQ=1Q [/itex]
    where Q is a generic column vector and 1 is the eigenvalue because we are
    spin up in the z direction. Or do I need everything in the x basis.
    But it seems like I first have to work in the z basis because we know it is spin up in the z direction.
     
  2. jcsd
  3. Dec 27, 2012 #2

    mfb

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    2016 Award

    Staff: Mentor

    If you can express "spin in z-direction" in the basis of spin in x-direction, you don't have to work with a basis of z-spin.
    The basis is just a mathematical tool - you can choose any basis you like (even y-direction or weird linear combinations of those, but that would be impractical).
     
  4. Dec 27, 2012 #3
    so i just need to write spin up in the z in the x basis.
    Im not really sure how to do that with spin-1.
    Do I use a rotation matrix.
     
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