I'm studying time dependent perturbation theory on Reed-Simon book "Method of modern mathematical physics, II". If one considers an Hamiltonian of the form $$H(t)=H_0+V(t)$$ the corresponding formal propagator is given by $$U(t,s)=e^{-itH_0}\tilde{U}(t,s)e^{isH_0}\,,$$ where $\tilde{U}(t,s)$ is the propagator associated to $\tilde{V} (t)=e^{iH_0t}V(t)e^{isH_0}$. How to prove that if $t\to [H_0,V(t)]$ is strongly continuous, then $U(t,s)$ is the actual propagator for $H(t)$? Any suggestions?
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1$\begingroup$ Cross-posted from math.SE as Time dependent perturbation theory $\endgroup$– მამუკა ჯიბლაძეJul 7, 2017 at 18:57
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