1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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...
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Fourier transforms
  1. Fourier Transform (Replies: 2)

  2. The Fourier transform (Replies: 1)

  3. Fourier transform (Replies: 2)

  4. Fourier Transform (Replies: 3)

  5. Fourier Transform (Replies: 1)