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I was just trying to confirm to myself that the following density operator $$\rho(t) = e^{-iHt/\hbar} \rho(0) e^{iHt/\hbar}$$ fulfills the Liouville-von Neumann equation: $$\frac{d}{dt}\rho(t) = - \frac{i}{\hbar} [H,\rho(t)]$$ where $[H,\rho(t)]$ denotes the commutator of the Hamiltonian with th...