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Expectation values must be real?

  1. Jun 27, 2006 #1
    Is it true that all expectation values must be real? So if I get an imaginary value, does it mean I made a mistake? Or it doesn't matter and I can just take the absolute value of the expectation?

    The momentum operator has an 'i' in it. But after doing, Psi*[P]Psi, I have an expression with 'i' which means I am left with an imaginary expectation value? What should I do?
  2. jcsd
  3. Jun 28, 2006 #2
    Absolutely. They are weighted averages over possible measurement outcomes. The outcomes are real, the weights (probabilities) are real, so the expectation value has to be real. By the way, this is why the operators associated with observables are self-adjoint. The eigenvalues of operators associated with observables are the possible outcomes of measurements. And eigenvalues of self-adjoint operators are real. See how things hang together?
  4. Jun 28, 2006 #3


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    I would say that with high probability, you need to go back and redo your calculation.

    The "i" in the operator should get eliminated by an i that appears when you apply d/dx to something that looks like exp(ix).

    The only time you might legitimately get a complex answer to something like this is when you are violating unitarity (if I recall correctly). That means that probability isn't being conserved, so your problem might involve a radioactive decay. But even then, you won't get a purely imaginary answer.

    By the way, there is a pretty good probability that this discussion will get banished to homework land. The basic idea is that if it's not interesting enough to make the local experts call each other names, then it must be homework.

    Last edited: Jun 28, 2006
  5. Jun 28, 2006 #4
    HAHA; I like the way you put it!
  6. Jun 29, 2006 #5
    And if it's interesting enough, it may get banished to the philosophy forum! :biggrin:
  7. Jul 8, 2006 #6
    Yup me too! Anyway check your calculations (as already pointed out...)
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