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Sequential measurements

  1. Feb 16, 2006 #1
    Hi,
    I really need help solving this problem, can you plzz help me with it?
    Here is the problem:
    An operator A, representing observable A, has two normalized eigenstates w1 and w2, with eigenvalues a1 and a2, respectively. Operator B, representing observable B, has two normalized eigenstates Q1 and Q2, with eigenvalues b1 and b2. The eigenstates are related by:
    w1=(3Q1+4Q2)/5, w2=(4Q1-3Q2)/5

    a) observable A is measure, and value a1 is obbtained . What is the state of the system after the measurement?
    b) If B is now measured, what are the possible results and what are their probabilites.
    c) Right after the measurement of B, A is measured again. What is the probability of getting a1?
     
  2. jcsd
  3. Feb 16, 2006 #2

    Galileo

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    This question simply tests your knowlegde of the postulates of QM. Refer to your book/notes about it, it describes the rules about how to calculate all the probabilities and stuff once you know the wave function.

    If you have trouble with understanding the postulates, just ask this forum. Otherwise, show your work on this problem.
     
  4. Feb 17, 2006 #3

    Galileo

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    (Assume the eigenvalues are nondegenerate)
    Question a) is about the 'projection postulate'. After a measurement the state collapses into the eigenstate corresponding to the measured eigenvalue.
    Question b) The probability of measuring a certain eigenvalue q_n is |<q_n|psi>|^2, where |q_n> is the eigenstate with eigenvalue q_n.

    It should be in your book. Please be more specific about what you don't understand.
     
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