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Fourier transformation: power spectrum

  1. Jan 7, 2009 #1
    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) (=[tex]\int[/tex][tex]\varphi\varphi^{*}[/tex]z):
    p([tex]\omega[/tex])=|[tex]\frac{1}{tf-ti}[/tex][tex]\int d(t)exp(-i\omega)[/tex]dt|[tex]^{2}[/tex]

    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([tex]\omega[/tex])=|[tex]\frac{1}{tf-ti}[/tex][tex]\int r(t)*cos(\theta)exp(-i\omega)[/tex]dt|[tex]^{2}[/tex]
    Thank you!
  2. jcsd
  3. Jan 7, 2009 #2
    I suggest looking up the Wiener Khinchin theorem.
  4. Jan 8, 2009 #3
    Thank you! :)
    Happy New Year!
  5. Jan 8, 2009 #4
    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!!
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