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Fourier transform of a Gaussian

  • #1

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.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Don't do that. Combine the exponentials, complete the square in x and do a change of variables.
 
  • #3
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.
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
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.
 

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