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Proving the expectation value of any eigenvalue function

  1. Mar 18, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-3-18_15-37-43.png

    2. Relevant equations
    upload_2017-3-18_15-38-16.png
    upload_2017-3-18_15-40-42.png

    3. The attempt at a solution
    When I take the second formula, multiply by it's conjugate and then by x and do the integral of the first formula, I get 0, and not L/2, for <x>. Am I missing a formula ?
    The complex conjugate of the exponential part multiplied by the exponential part simplifies to 1, and when I do the integral I end up with 0.
     
  2. jcsd
  3. Mar 18, 2017 #2

    kuruman

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    What are your integration limits?
     
  4. Mar 18, 2017 #3
    -infinity and +infinity, as in the first formula (the orange background)
     
  5. Mar 18, 2017 #4

    kuruman

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    What is the size of the "box" the particle is in?
     
  6. Mar 18, 2017 #5
    L? so would it be from 0 to L ?
     
  7. Mar 18, 2017 #6

    kuruman

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    Right. The particle is confined from 0 to L.
     
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