# Fourier transformation: power spectrum

1. Jan 7, 2009

### xylai

Lots of works about the high-order harmonic generation in the intense laser-atom physics obtain the harmonic spectrum by Fourier transformation of the dipole moment d(t) (=$$\int$$$$\varphi\varphi^{*}$$z):
p($$\omega$$)=|$$\frac{1}{tf-ti}$$$$\int d(t)exp(-i\omega)$$dt|$$^{2}$$

Here, I want to use the Monte-Carlo method to generate the Harmonics. The trajectory r(t) of an electron in 3D Hydrogen system can be get. Then how can I obtain the harmonic spectrum for one electron? Can I use the Fourier transformation of r(t) directly?
p($$\omega$$)=|$$\frac{1}{tf-ti}$$$$\int r(t)*cos(\theta)exp(-i\omega)$$dt|$$^{2}$$
Thank you!

2. Jan 7, 2009

### IPart

I suggest looking up the Wiener Khinchin theorem.

3. Jan 8, 2009

### xylai

Thank you! :)
Happy New Year!

4. Jan 8, 2009

### xylai

Yesterday, I look up the Wiener Khinchin theorem. (http://en.wikipedia.org/wiki/Wiener–Khinchin_theorem)
The paper shows what the Wiener Khinchin theorem is and how we can use this theory.
Here I have another question:
Usually, the electron moves around the proton in the real space. x(t) is in the 3 dimensional spatial coordinate.
If we want to use the Wiener Khinchin theorem, first we need calculate the autocorrelation function.
My question is if x(t) is in the 3 dimensional spatial coordinate, how can we calculate the autocorrelation function?
Thank you!!