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Integral of a gaussian

  1. May 11, 2015 #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.
  2. jcsd
  3. May 12, 2015 #2


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    Is this homework?
  4. May 12, 2015 #3
    No. I'm trying to learn quantum mechanics and this thing keeps popping up.
  5. May 12, 2015 #4


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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?
  6. May 12, 2015 #5


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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.
    Last edited: May 13, 2015
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