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Homework Help: 2 quantum questions

  1. Nov 5, 2007 #1
    1. The problem statement, all variables and given/known data

    1. Consider a beam of z-oriented electrons, 80 % up, 20 % down which is passed through an x-oriented Stern-Gerlach machine. What percentage of electrons are measured in the +/- x-directions?

    2. Consider deuterium. Nuclear spin = 1 with 1 electron orbiting in the n =1 state. Write down the ket for the total angular momentum [itex]|\frac{3}{2} \frac{1}{2}\rangle[/itex] as a linear combination of composite states.

    3. The attempt at a solution

    1. I write the eigenstates of [itex]S_z[/itex] in a superposition [itex]\sqrt{0.8} (1,0)^T + \sqrt{0.2} (1,0)^T[/itex] (where T denotes transpose) and set it equal to an linear combination of the [itex]S_x[/itex] eigenstates [itex]a(1,1)^T + b(1,-1)^T[/itex]. Solving for a and b I get 45 % and 5 %. Interestingly they don't add to 100 % which was what I was expecting. Is this physically reasonable?

    2. Do I just write [itex]|3/2,3/2\rangle = |1,1\rangle |1/2,1/2 \rangle[/itex] and apply lowering operators? I can do this because l = 0 so there is no orbital contribution to the angular momentum right?
     
  2. jcsd
  3. Nov 5, 2007 #2

    Meir Achuz

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    "Consider a beam of z-oriented electrons, 80 % up, 20 % down"

    This does not mean the WF you wrote. Each electron would be either pure up or pure down, and 1/2 would go each way in the z direction, just as for an umpolarized beam.
    A problem here is that the usual SG experiment does not work for charged particles.
     
  4. Nov 5, 2007 #3

    Meir Achuz

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    You are correct for 2.
     
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