Is the Fourier transform of the function correct?

Question

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?

Answer 1

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

In short: your result is correct.