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I Finding probability of changing states

  1. Jul 15, 2016 #1
    I am following the derivation shown in this link on adiabatic passage.

    I have posted one part below:

    Screen Shot 2016-07-15 at 11.53.04 AM.png

    I am simply wondering how this expression was derived and how it indicates the probability of being in a state that is different from the initial state? How exactly is this represented by:

    $$ \langle \hat{U}^\dagger(t_1,t_0)\hat{U}(t_1,t_0)\rangle - \langle \hat{U}^\dagger(t_1,t_0)\rangle\langle \hat{U}(t_1,t_0)\rangle $$
  2. jcsd
  3. Jul 15, 2016 #2

    Paul Colby

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    Gold Member

    The last term in your last expression is the probability that you will remain in the initial state. The first term is 1 by unitarity. The difference of these terms is the total probability of not being in the initial state.
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