Expectation Value of Momentum

  • #1
atomicpedals
209
7
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]?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Of course you would apply it to ψ. What else?
 
  • #3
atomicpedals
209
7
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]
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
621
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]

Yes. That's it.
 
  • #5
atomicpedals
209
7
Right on, thanks.
 

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