- #1

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^{p}e

^{-x2}e

^{ix}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.

- Thread starter Ananthan9470
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- #2

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Is this homework?^{p}e^{-x2}e^{ix}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.

- #3

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No. I'm trying to learn quantum mechanics and this thing keeps popping up.Is this homework?

- #4

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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.

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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