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Expectation value of a combination of operators

  1. Mar 23, 2015 #1


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    1. The problem statement, all variables and given/known data

    I will denote operators by capital letters. The question is calculate

    <p | XXPP | x> / <p | x >
    2. Relevant equations
    X |x> = x |x> P |p> = p |p> P |x> = -i(hbar)d/dx X |p> = i(hbar)d/dp

    3. The attempt at a solution
    If I start on the RHS and take PP out I get -(hbar)^2 d^2/dx^2 outside the bracket then I can take the XX outside if it operates on the |x> as x^2 but to be honest i'm not getting anywhere
  2. jcsd
  3. Mar 23, 2015 #2
    Use the canonical commutation relation between the operators X and P. With that you can reverse the order of the operators in the expectation value.
  4. Mar 23, 2015 #3


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    Thanks. I finally got the answer.
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