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Expectation Value of Momentum

  1. Dec 18, 2011 #1
    I've managed to get myself confused on a seemingly simple point of mathematics. When I calculate the expectation value of momentum in quantum mechanics

    [tex]<p>=\int{\psi* \frac{\hbar}{i} \frac{d}{dx} \psi dx}[/tex]
    To what should I be applying the derivative? [itex]\psi[/itex]?
     
  2. jcsd
  3. Dec 18, 2011 #2

    Dick

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    Of course you would apply it to ψ. What else?
     
  4. Dec 18, 2011 #3
    Order of operation would rule out complex conjugate of [itex]\psi[/itex]. So, instead of being like <x> which can simplify to

    [tex]<x>=\int{|\psi|^{2}xdx}[/tex]
    it would instead be
    [tex]<p_x>=\int{\psi * \frac{\hbar}{i} \frac{d \psi}{dx} dx}[/tex]
     
  5. Dec 18, 2011 #4

    Dick

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    Yes. That's it.
     
  6. Dec 18, 2011 #5
    Right on, thanks.
     
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