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States

Using Eq. (VI.3.3), in the interaction picture
$\displaystyle \vert\Psi(t)\rangle_I$ $\displaystyle \equiv$ $\displaystyle e^{iH_0 t} \vert\Psi(t)\rangle = e^{iH_0 t} U(t,t_0) \vert\Psi(t_0)$  
  $\displaystyle =$ $\displaystyle e^{iH_0 t} e^{-i{H_0}t} \tilde{U}(t,t_0)e^{i{H_0}t_0} \vert\Psi(t_0)\rangle$  
  $\displaystyle =$ $\displaystyle \tilde{U}(t,t_0) \vert\Psi(t_0)\rangle_I.$ (3.24)


Subsections
Tobias Brandes 2005-04-26