Symbol i

The passage around this formula

…the relabeling. But $\dot U$ $U^\dagger$ = i$\omega_r$$\sigma_z$/2 exactly, giving $H_c(t) = H_f + i\hbar\Big(i\frac{\omega_r}{2}\sigma_z\Big) = \frac{\hbar(\omega_0 - \omega_r)}{2}\sigma_z$. the detuned Hamiltonian that governs spin precession in a frame rotating with an applied field — the identical construction I. I. Rabi used to analyze spin behavior in a gyrating magnetic field in 1937 [ 14 ] . Two checks confirm the recovery is exact rather than incidental: at $\omega_r$ = 0 , the non-rotating case, $\Delta_{\rm frame}$ $\equiv$ 0 and $H_c$ = $H_f$ , the already-verified baseline; at $\omega_r$ = $\omega_0$ , exact…

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