= Magnus expansion
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{title2=$U(T)=\exp(\Omega_1+\Omega_2+\cdots)$}
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For $\dot U=A(t)U$ and $U(0)=I$, the Magnus expansion writes the logarithm of the propagator as iterated integrals of <commutators>. Its first terms are $\Omega_1=\int_0^TA(t)dt$ and $\Omega_2=\tfrac12\int_0^Tdt\int_0^tds\,[A(t),A(s)]$. For a <Quantum Hamiltonian>, $A=-iH/\hbar$, so a noncommuting time-dependent control has corrections beyond the exponential of its integrated <Quantum Hamiltonian>. This formula is a local convergent expansion under suitable smallness conditions, or a formal expansion; it must not be assumed globally convergent for arbitrary pulse durations.
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