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I am asked to calculate the Fourier transform of the function $$e^{-\frac{x^2}{2a^2}}, a>0$$ $$$$ After calculations I have found the following: $$a \sqrt{2 \pi} e^{-\frac{a^2 k^2}{2}}$$ $$$$ Is this correct?

Mary Star
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    Maybe, maybe not. Depends on which definition of Fourier transform you use; there are several versions of it. – user127096 Apr 14 '14 at 21:27
  • @cheapeffectivedietpills I use this definition: $$\widetilde{f}(k)=\int_{-\infty}^{+\infty}{f(x)e^{-ikx}}dx$$ – Mary Star Apr 14 '14 at 21:48

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Check out Wolfram|Alpha with FourierParameters to specify your version of the Fourier Transform.

In short: your result is correct.

Klaas van Aarsen
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