I am following the derivation shown in this link on adiabatic passage.(adsbygoogle = window.adsbygoogle || []).push({});

I have posted one part below:

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:

$$ \langle \hat{U}^\dagger(t_1,t_0)\hat{U}(t_1,t_0)\rangle - \langle \hat{U}^\dagger(t_1,t_0)\rangle\langle \hat{U}(t_1,t_0)\rangle $$

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# I Finding probability of changing states

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