Derivation of momentum operator / origin of -ih d/dx

  • Thread starter Juqon
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  • #1
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Homework Statement


In the derivation of the momentum operator: Why is this equal?


Homework Equations


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


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.
 
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Answers and Replies

  • #2
vela
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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.
 
  • #3
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Now I see it. Thanks!
 

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