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Calculating expectation value

  1. Aug 16, 2010 #1
    Let A be an observable (opeator), and we're assuming that for a given state psi(x), the value of A is given by A acting on psi(x), namely - A|psi>.
    Also we assume that - P(x) = |psi(x)|^2
    So, I'de expect the Expectation value of A to be defined like so:
    <A> = Integral[-Inf:+Inf]{ P(x) A psi(x) dx} = Integral[-Inf:+Inf]{ |psi(x)|^2 A psi(x) dx} , which is not <psi|A|psi>, and that's clearly not right. where did i go wrong here?
     
  2. jcsd
  3. Aug 16, 2010 #2

    jtbell

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    Staff: Mentor

    No. [itex]A|\psi\rangle[/itex] is not a value. It's another state, in general.

    If [itex]|\psi\rangle[/itex] happens to be an eigenstate of the operator A, then [itex]A|\psi\rangle = a|\psi\rangle[/itex], where a is an eigenvalue of the operator A.
     
  4. Aug 16, 2010 #3
    got it, thank you!
     
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