I need some help with this also:

Prove that :

FourierTransform[e^(-ax^2)]=(sqrt[Pi/a]) e^(-ω^2/4a)

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- October 31st 2006, 06:19 AMjmytilproblem on Fourier transforms
I need some help with this also:

Prove that :

FourierTransform[e^(-ax^2)]=(sqrt[Pi/a]) e^(-ω^2/4a) - October 31st 2006, 11:13 AMCaptainBlack
Put

Differentiate:

Now take FTs of both sides and apply the derivative rules to the forward

and backwards transform:

so we have satisfies the ODE:

and all one now has to do is show that the suggested form for satisfies

this equation (or you could just solve the equation - it's of variables separable type).

(there is at least one other way of doing it, but that requires Cauchy's integral theorem from complex analysis)

RonL