= Quantum rotating frame
{title2=$H_{\mathrm r}=R^\dagger HR-iR^\dagger\dot R$}
A time-dependent <unitary operator> $R(t)$ defines transformed <quantum states> by $|\psi_{\mathrm r}\rangle=R^\dagger|\psi\rangle$. Substituting $|\psi\rangle=R|\psi_{\mathrm r}\rangle$ into the <Schrödinger equation> gives the displayed transformed <Hamiltonian operator>, in units $\hbar=1$. If $R=e^{-itH_0}$ for constant $H_0$, this becomes $H_{\mathrm r}=R^\dagger HR-H_0$. Removing a common nuclear <Zeeman energy> with $H_0=\omega(ZI+IZ)/2$ leaves an isotropic <Heisenberg model> coupling unchanged, because it commutes with the generator of the common rotation. Removing two unequal nuclear frequencies instead makes their exchange terms oscillate at the difference frequency.
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