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Math Help - Solution Using Fourier Transform.

  1. #1
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    Solution Using Fourier Transform.

    Hi all.
    Plz find attached the word file. Can anyone help me in finding how can I get the equation 4 i.e. solution by using equations 1,2 and 3 ?
    Thanks.
    Attached Files Attached Files
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  2. #2
    A Plied Mathematician
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    Word files are generally frowned upon in this forum. A lot of members won't open Word files because of possible viruses in macros. Can you convert to pdf?
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  3. #3
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    Dear Ackbeet,
    Plz find the pdf here. Solution Using Fourier Transform.-problem.pdf
    Thanks.
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  4. #4
    A Plied Mathematician
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    Thanks for posting a pdf. I have a question: what is the question? What are you being asked to do here? There doesn't seem to be any sort of request here. Prove equation (4)?
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  5. #5
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    Dear Ackbeet.
    You are right. Equation 4 needs to be proved.
    Thanx.
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  6. #6
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    Very well, then. It looks like a straight-forward integration problem, then. You've got to plug things into things, and then plug those into things. So, for example, you have

    \displaystyle{U(0,T)=\exp\left(-\frac{T^{2}}{2T_{0}^{2}}\right),} but also

    \displaystyle{\tilde{U}(0,\omega)=\int_{-\infty}^{\infty}U(0,T)\exp(i\omega T)\,dT.}

    Taken together, you've got

    \displaystyle{\tilde{U}(0,\omega)=\int_{-\infty}^{\infty}\exp\left(-\frac{T^{2}}{2T_{0}^{2}}\right)\exp(i\omega T)\,dT.}

    All I've done so far is plug U(0,T) into the expression for \tilde{U}(0,\omega), right?

    Now, this is a doable integral as is. Do you know how to integrate Gaussian integrals?
    Last edited by Ackbeet; August 26th 2010 at 03:14 AM. Reason: Grammar.
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