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Fourier transforms

  1. Dec 9, 2013 #1
    1. We consider the on shell wave packet:
    [tex]\varphi(t,x)=\int\frac{dk}{2\pi}exp(-\frac{(k-k_{0})^{2}}{\Delta k^{2}}+ik(t-x))dk
    [/tex]

    I need to show it is proportional to:
    [tex]exp(ik_{0}(t-x)-\frac{\triangle k^{2}}{4}(t-x)^{2})dk[/tex]
    through a fourier transform of the gaussian


    3. I used a fourier transform of the form e^(ikx) but this doesn't seem to give me the right answer as I end up with something proportional to [tex]exp(-\frac{(k-k_{0})^{2}}{\triangle k^{2}}+ikt)dk[/tex] before integrating
     
  2. jcsd
  3. Dec 9, 2013 #2

    vela

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    Show us what you think the integral for ##\varphi(t,k)## is.
     
  4. Dec 9, 2013 #3
    Solved it! :-)...

    However I now need to solve this:

    [tex]\int\frac{dk}{2\pi}exp(-\frac{(k-k_{o})^{2}}{\triangle k^{2}}+ik(pt-x) [/tex]


    where [tex] p=1-\frac{h_{00}}{2}-h_{01}-\frac{h_{11}}{2}[/tex]

    by using fourier transforms
     
  5. Dec 9, 2013 #4
    Solved this one too now :-)

    Not sure how to graph it though...
     
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