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Anyone handy with Fourier transforms?

  • 15-01-2012 08:13PM
    #1
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭


    I'm wondering what the fourier transform of 1/|r1 - r2| is, where

    |r1 - r2| = square root of {(x2 - x1^2) + (y2-y1)^2 + (z2-z1)^2}

    Normally it is just 4 Pi / K^2, but there are two catches.

    The first is not much of an issue: 1/|r1 - r2| is only defined over a region of fine volume V = {0,1}{0,1}{0,1}. A box, in other words. That's no big deal. The transform becomes

    tex2png--10.cgi?\frac{1}{8}%20\int_{-1}^{1}%20\int_{-1}^{1}%20\int_{-1}^{1}%20\frac{e^{-i\mathbf{g}\cdot%20\mathbf{r}}}{|\mathbf{r}|}%20d\mathbf{r}

    Click

    which can be numerically solved.

    What I am stuck on is how the above form of the transform is changed when |r1-r2| is

    square root of {(x2-x1)^2 + A (y2-y1)^2 + B (z2-z1)^2}

    where A and B are positive real numbers.


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