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What is the Fourier transform of this function ?

  1. Mar 19, 2014 #1
    Hi, I have problems finding out the Fourier transform of the following function,

    1/\sqrt{q^2 + m^2}, where m\neq 0 denotes a parameter.

    It seems easy, but I don't know how. Could anybody show me how to do it ?

    Thanks in advance.

    hiyok
     
    Last edited: Mar 19, 2014
  2. jcsd
  3. Mar 20, 2014 #2

    Simon Bridge

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    $$f(q)=\frac{1}{\sqrt{q^2+m^2}}\\ \mathcal{F}(p)=\int_{-\infty}^\infty \frac{e^{-2\pi iqp}}{\sqrt{q^2+m^2}}\;\text{d}q$$ ... this correct?
    i.e. you want the forward fourier transform...

    Please show your best attempt.
     
    Last edited: Mar 20, 2014
  4. Mar 20, 2014 #3
    Yes, that is exactly what I meant.

    I tried to make a contour and evaluate the residue around the pole q=im. But the order of this pole is not integer. I don't know how to proceed.

    Thanks
     
  5. Mar 20, 2014 #4

    Simon Bridge

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  6. Mar 20, 2014 #5
    Thanks a lot for your useful message. I'll look into your link.

    I met this integral when trying to find out the Green's function for a graphene ribbon.
     
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