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Homework Help: Measuring Spin - wave function collapse

  1. Apr 26, 2010 #1
    It is my understanding that a measurement of [tex] S_z [/tex] followed by a measurement of [tex] S_y [/tex] will result in a particle which is in an eigenstate of [tex] S_y [/tex]. But it appears that a measurement of say [tex] S_y [/tex] followed by a measurement of [tex] S_x [/tex] results in zero. I see this from a question in which im asked to find the expectation value of [tex] S_x [/tex] for a particle in an eigenstate of [tex] S_y [/tex] and my result is zero. But for [tex] S_z [/tex] it is non zero.
    I dont understand why this is so. Could someone help me understand why we find non zero [tex] S_z [/tex] values but zero [tex] S_x [/tex] values for a partilce in an [tex] S_y [/tex] eigenstate.

    Thanks in advance.

    B
     
  2. jcsd
  3. Apr 26, 2010 #2

    vela

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    Taking a measurement is not the same as finding the expectation value. If you take a measurement of Sx or Sz, you'll always get 1/2 or -1/2 (in units of h-bar). The expectation value is what you'd expect if you took many measurements and averaged the results.
     
  4. Apr 30, 2010 #3
    Ok. I understand now. Thank you Vela.

    It makes sense that the expectation value in the [tex] S_z [/tex] direction is NOT zero even if we are in a quantum state of [tex] S_x [/tex] or [tex] S_y [/tex] since it is the "preferred" direction I suppose, while [tex] S_x [/tex] and [tex] S_y [/tex] should exhibit zero expectation if we are in the [tex] S_z [/tex] eigenstate as they sort of rotate around [tex] S_z [/tex].
    or something like that. cheers.
     
  5. Apr 30, 2010 #4

    vela

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    If you're in an eigenstate of Sx, the preferred direction is along the x-axis. You should find the expectation values of Sy and Sz to be zero.

    Keep in mind that x, y, and z are just labels we use to keep things straight. There's nothing intrinsically special about the z-axis.
     
  6. Apr 30, 2010 #5
    oh ok. now I think I really do understand. Source of confusion: hypothetical triple stern-gerlach experiment which exhibits that taking a measurement of Sx on an Sz eigenstate beam would produce 2 more beams in eigenstates of Sx. Obviously 2 resulting beams in the up and down eigenstates of Sx still amount to a zero expectation value.

    Thanks again Vela, and if your interested in helping me with another unrelated question regarding GR and the cylinder condition that would be great as well : https://www.physicsforums.com/showthread.php?t=399738

    cheers.

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