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Stern-Gerlach spin probability

  1. May 9, 2014 #1
    So I've just been reading about the Stern-Gerlach apparatus/experiment and had some questions about the half spin probabilities...

    First let's say a collection of spin-half particles are sent through a S-G apparatus (which I know measures the z component of particles spin angular momentum) it is known that the results are always either 1/2ħ or -1/2ħ. And though the result cannot be predicted before it has been calculated by quantum mechanics that the probability of getting 1/2ħ is 0.75. So then what is the probability of getting the result -1/2ħ? I saw some sites referring to cosine and sine while others said it was 1 so it confused me

    So for example if say 20000 particles are sent through, how many will have a z component equal to -1/2ħ (I'm thinking 50%?) then what would be the average z component of spin for all the particles?
  2. jcsd
  3. May 9, 2014 #2


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    It is a binary measurement. If you are not measuring +1/2 you are measuring -1/2 and the probability should add up to one. Thus, if you know that the probability of measuring 1/2 is 75%, then the probability of measuring -1/2 must be 25%.

    Of course, in order to have such a setup, the incoming spins must already be polarized or the probabilities will be 50-50.
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