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I'm attempting to prove that [tex] i \frac{d \xi (t)}{dt}=[\xi(t),H(p,q ; t)] [/tex] where the Hamiltonian is explicitly time-dependent, in general. We also have some unitary U(t) which generates time-evolution. I wrote up a quick proof but realized afterward that I had assumed that H and U(t) commute. But this isn't true is it? My reasoning is this: U(t) flows the system though time, and since H depends explicitly on time, it is no longer a constant of the motion. Therefore, H is not conserved and [U,H] does not vanish. Is this right?