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Fourier transform of a Gaussian

  1. Mar 10, 2007 #1
    1. The problem statement, all variables and given/known data

    I need to have the Fourier transform of a Gaussian

    2. Relevant equations



    3. 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.
     
  2. jcsd
  3. Mar 10, 2007 #2

    Dick

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    Don't do that. Combine the exponentials, complete the square in x and do a change of variables.
     
  4. Mar 10, 2007 #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.
     
  5. Mar 10, 2007 #4

    Dick

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    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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