Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time evolution of a state. (a missing t)

  1. Feb 22, 2015 #1

    naima

    User Avatar
    Gold Member

    Hi PF there is one thing that i cannot understand here.
    Please look at eqn 1068
    I try to compute the first term (without ##V^\dagger##)
    I get someting like
    ##c_f (t) =-i/\hbar exp [i(\omega + \omega_{fi})t/2] \frac{sin(\omega + \omega_{fi})t/2}{(\omega + \omega_{fi})/2} \}##

    Unlike eqn 1071 a "t" is lacking under the sine and i cannot write it as a sinc function.

    Could you help me? I do not see my mistake.
    (I can write my intermediate formulas)
     
    Last edited: Feb 22, 2015
  2. jcsd
  3. Feb 22, 2015 #2

    naima

    User Avatar
    Gold Member

    We begin with a ##\int_0^t xxx... dt' term##
    With a change of variables t"" = t' -t/2 we get
    ##\int_{-t/2}^{t/2} exp[i \Omega (t"" + t/2)] dt""##
    ##= exp[i \Omega t/2]\int_{-t/2}^{t/2} exp[i \Omega t""] dt""##
    In the integral the odd i sin function gives no contribution so we have
    ##= exp[i \Omega t/2]\int_{-t/2}^{t/2}cos (\Omega t"") dt""##
    so we finish with a ##sin (\Omega t/2) / (\Omega/2) ##
    But the real formula has a ##sin (\Omega t/2) / (\Omega t/2) ##
    Where does this t come from?
     
    Last edited: Feb 22, 2015
  4. Feb 22, 2015 #3

    naima

    User Avatar
    Gold Member

    Sorry I did not see that in the link we had ##c_n(t) = it/\hbar .....##
    I have no more problem with the formula :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Time evolution of a state. (a missing t)
  1. Evolution of States (Replies: 0)

Loading...