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Homework Help: Derivation of momentum operator / origin of -ih d/dx

  1. Aug 13, 2011 #1
    1. The problem statement, all variables and given/known data
    In the derivation of the momentum operator: Why is this equal?

    2. Relevant equations
    [PLAIN]http://img268.imageshack.us/img268/4575/momentumoperatorderivat.png [Broken]

    3. The attempt at a solution
    I thought maybe the integral is executed, but the integral sign stays.
    One p vanishes, the momentum operator itself shows up.
    You would really expect this in a derivation of p, but dp stays.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 13, 2011 #2


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    There's two steps in there. First, you can write
    [tex]p \exp\left(\frac{ipx}{\hbar}\right) = \frac{\hbar}{i}\frac{\partial}{\partial x}\exp\left(\frac{ipx}{\hbar}\right)[/tex]
    Then you interchange the order of integration and differentiation.
  4. Aug 13, 2011 #3
    Now I see it. Thanks!
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