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Checking if Momentum Operator is Hermitian - Integration

  1. Dec 11, 2014 #1
    1. The problem statement, all variables and given/known data

    I'm checking to see if the momentum operator is Hermitian. Griffiths has the solution worked out, I'm just not following the integration by parts.

    2. Relevant equations

    int(u dv) = uv - int(v du)

    3. The attempt at a solution

    I've attached an image of my work.

    It seems there should be an additional 'dx' with my 'v' term, but then the 'uv' portion would have a 'dx', which wouldn't make much sense to me.

    Thanks for your time.
     

    Attached Files:

  2. jcsd
  3. Dec 11, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    If you set ##u = f^*##, then
    $$
    \frac{du}{dx} = \frac{df^*}{dx}
    $$
    hence
    $$
    du = \frac{df^*}{dx} dx
    $$
     
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