- #1

- 32

- 0

^{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.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Ananthan9470
- Start date

- #1

- 32

- 0

- #2

- 20,011

- 11,388

^{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.

Is this homework?

- #3

- 32

- 0

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

- #4

- 20,011

- 11,388

Can you integrate it without the complex exponential?

- #5

mathman

Science Advisor

- 8,022

- 526

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.

Last edited:

Share: