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The quantum mechanical time evolution operator governs how observables and/or states evolve during finite time steps, and is always unitary. Use this tag for questions about the time evolution operator, or the different equations of motion in the Schrödinger/Heisenberg/Dirac pictures. For time-independent Hamiltonians, the time evolution operator is simply exp(-iHt).
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Time evolution operator for Hamiltonien with scalar commutator at different times
Let $H(t)$ be a time-dependent Hamilton-operator and assume that $[H(t),H(t')] = f(t,t')\, \mathrm{id}_\mathcal{H}$. Is there a closed formula for its time-evolution operator?
I tried deducing an exp …