{title2=$\theta=\hbar^{-1}\int\Omega(t)\,dt$}

= Pulse area
{synonym}

For a fixed dimensionless <Hermitian operator> $A$ driven by $H(t)=\Omega(t)A$, all instantaneous generators commute. The exact <unitary operator> is $U(T)=\exp(-i\theta A)$, so the area, rather than the detailed envelope, fixes the rotation. For $A^2=I$, it is $\cos\theta\,I-i\sin\theta\,A$. This convention uses the <Quantum Hamiltonian> coefficient directly; a convention with $\hbar\Omega_R A/2$ instead has $\theta=\tfrac12\int\Omega_Rdt$.


 Quantum pulse area (source code)