Integral of a gaussian

  • #1
I need to evaluate ∫xp e-x2 eix dx from -∞ to ∞ Can someone please give me some pointers on how to do this? I am completely lost. I just need some hints or something.
 

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  • #2
PeroK
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I need to evaluate ∫xp e-x2 eix dx from -∞ to ∞ Can someone please give me some pointers on how to do this? I am completely lost. I just need some hints or something.
Is this homework?
 
  • #3
Is this homework?
No. I'm trying to learn quantum mechanics and this thing keeps popping up.
 
  • #4
PeroK
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You'll get a better response if you post it in homework. Even if you're learning on your own, it still counts.

Can you integrate it without the complex exponential?
 
  • #5
mathman
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To get you started, if p is even you need only cosx. If p is odd you need only isinx, where [itex]e^{ix}=cosx+isinx[/itex].
Next integrate by parts to reduce exponent from p to p-1, and continue until you get p = 0.
At the end you should have [itex]\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}cosxdx[/itex].

As an afterthought, it might be easier to start from
[itex]\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}cosxdx[/itex]. Then integrate by parts to increase the exponent of x.
 
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