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Fourrier transform of cos

  1. May 29, 2014 #1
    Fourier transform of density matrix of cos(x+y)*cos(x-y)

    I would like to know whether there exists a solution to the following integral,

    [tex] \frac{1}{\pi} \int\limits_{-\infty}^{\infty} \cos(x+y)^\alpha \cos(x-y)^\alpha e^{2ipy} [/tex]

    The above expression is the Fourier transform of the off-diagonal elements of the density matrix,

    [tex] \rho = \cos(x+y)^\alpha \cos(x-y)^\alpha [/tex]

    Any advice, or reference to books/articles, would be greatly appreciated.
    Last edited: May 29, 2014
  2. jcsd
  3. May 29, 2014 #2


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    Gold Member

    Start by defining the domain for α.
    Google "Fourier integral tables" should help.
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