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 transform

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data

    An atom raised at t=0 to an excited state with energy [itex] E_0= \hbar \omega_0 [itex] has the time dependence [itex] T(t)=\frac{1}{\sqrt \tau}e^{-t/ 2 \tau} [itex] for t>0 and T(t)=0 for t<0. Thus the probability of being in an excited state decays exponentially with time.

    [itex] T(t)^2= \ frac {1} {\tau} e^ {-t/ \tau} [itex]

    a.) Find the transform b(w) of T(t).

    ('w' is omega, frequency)

    b.) Plot |b(w)|^2 as a function of w.

    c.) show that b(w) traces a circle on the complex plane as w runs from well below w_0 to well above it.

    2. Relevant equations

    [tex] b(\omega)=\frac{1}{\sqrt{2 \pi}}\int{T(t)e^{i \omega t}} [/tex]

    The integral runs from -infinity to infinity.

    3. The attempt at a solution

    [tex] b(\omega)=-\frac{1}{\sqrt{2 \pi \tau}}\frac{1}{i(\omega - \omega _0)-\frac{1}{2 \tau}} [/tex]

    When I do plot for part b, I get exponential incerase. Does that sound right?

    But when I do part (c), I don't get a circle nor elipse.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Fourier transform
  1. Fourier transform (Replies: 6)

  2. Fourier Transforms (Replies: 3)

  3. Fourier transformation (Replies: 1)

  4. Fourier transforms (Replies: 5)

  5. Fourier transform (Replies: 1)