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Subsequent Measurements

  1. Aug 25, 2010 #1
    So i've gotten myself stumped the other day.

    Suppose I have an electron in a magnetic field, where the field is oriented along the x-axis, than I know that the H-matrix/operator is defined as -g*|B|*h/2 *Sx. Now say I know that I have a wave-function in a known initial state-vector, lets call is A. I can express A as a linear combination of the two eigenvectors associated with the H-matrix. Ok that seems fine, I can make a measurement of <A|H|A> and that's great. And if I want to let the system evolve in time I just stick the energy eigenvalues into the evolution (exp[-iEt/h]). But lets say I want to make a measurement of Sz now that I have the energy of the system after a short time.

    Now I get myself confused, since H commutes with any S can't I just take the state-vector A, expressed as a linear combination of H's eigenvectors, and operate Sz on A to determine the expectation of Sz? When I ask some of my classmates we end up having a disagreement on whether or not this a viable measurement or not, and if it is if I am adding complications or not.

    Any help on clearing this up would be great.

  2. jcsd
  3. Aug 27, 2010 #2
    I guess you did not get any reply till now, because your question is not very clear. For instance you say "I can make a measurement of <A|H|A> ". Now, <A|H|A> is an expectation value. It is neither a measurement nor a result of a single measurement. Perhaps if you edit your question so that it becomes really precise, then you will get some feedback.
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