Fourier transform of exp(-ax²)

[Kolahal Bhattacharya]

Homework Statement

I need to have the Fourier transform of a Gaussian

Homework Equations

The Attempt at a Solution

∫(exp[-ax^2])(exp[-ikπx]) dx

I tried by braking the last exponential into sine and cosine terms.The sine term is odd and it cancels.Then,I cannot evaluate the remaining part.Please help.

 

[Dick]

Don't do that. Combine the exponentials, complete the square in x and do a change of variables.

 

[Kolahal Bhattacharya]

OK,what I am getting is a standard gamma function type of integral(that I can find) and the 2nd part is an ordinary constant exponential.
So,is this what you meant?I hope there is no more subtlity in this problem.

 

[Dick]

You should be getting that the Fourier transform of a gaussian in x is a constant times a gaussian in k. No, it's not subtle.