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Question if expectation value is considered a measurement?

  1. Sep 13, 2012 #1
    Hello,

    I was just curious about expectation values. One of the postulates of quantum mechanics state:
    The only possible results of a measurement is an eigenvalue of the operator.

    Now, is the expectation value considered a measurement, thus considered an eigenvalue?

    Thanks!
     
  2. jcsd
  3. Sep 13, 2012 #2
    An expectation value is a weighted average of all of the eigenvalues. So it may or may not actually be a valid eigenvalue itself.

    As an example, the X component of the spin operator has two eigenvalues: -1/2 and 1/2. However, if you take the X expectation value of a Z state (which is a linear combination of both of those eigenstates), the expectation value will be 0, since both -1/2 and 1/2 states appear in equal combination. 0 is not actually a valid eigenvalue of the X operator, but it's the average of the two actual eigenvalues.
     
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