= Constant pulse-axis condition for removing time ordering
{title2=$[H(t),H(s)]=0\Longrightarrow U(T)=e^{-i\int_0^TH(t)dt/\hbar}$}
For $H(t)=\Omega_1(t)A+\Omega_2(t)B$ with fixed noncommuting <Hermitian operators>, $[H(t),H(s)]=[\Omega_1(t)\Omega_2(s)-\Omega_2(t)\Omega_1(s)][A,B]$. A constant ratio of the envelopes is sufficient to remove <time ordering>. Independently changing that ratio generally produces <commutator> corrections in the <Magnus expansion>, and a product of successive pulses need not equal the exponential of their summed areas.
Back to article page
