Knowing that the Fourier transform of the function $y\left ( t \right )= e^{-t^{2}}$ is equal to $\sqrt{\pi}e^{-\frac{\omega ^{2}}{4}}$ I then proceeded using the the derivative rule $$\mathcal {F}\left [ te^{-t^{2}} \right ]=-i\sqrt{\pi} \frac{\omega }{2}e^{-\frac{\omega ^{2}}{4}}$$ However my answer is not listed as a possible solution. I tried tackling this problem by using definition, but there appeared some nasty integrals.
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1Your approach is correct, maybe you just made some computation mistake. – Chee Han Jun 10 '15 at 16:21
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Your answer is correct. What were the listed answers? – Mark Viola Jun 10 '15 at 16:26
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Make sure you are using a different definition of fourier transform. Does it have a similar form? – Gappy Hilmore Jun 10 '15 at 16:27
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I will type them out later. The do look similar, indeed, differing only by a factor a factor of $\sqrt2$ – Shemafied Jun 10 '15 at 16:58