= Solution
The populations give
$$
\boxed{\langle S_z\rangle=\frac{\hbar}{2}(c^2-s^2)=\frac{\hbar}{2}\cos(\Omega t),\qquad
\Omega=2\omega=\frac{geB_x}{2m}}.
$$
Together with $\langle S_y\rangle=(\hbar/2)\sin(\Omega t)$, this describes <Larmor precession> of a <spin> initially perpendicular to the field. The positive angular <frequency> is $|\Omega|$; the sign specifies the rotation sense through $d\langle\mathbf S\rangle/dt=\gamma\langle\mathbf S\rangle\times\mathbf B$. The factor of two between the <spinor> amplitudes and the measured <spin> is essential. The model with <quantum coherence> predicts no decay; <spin relaxation> or <dephasing> in a real solid can damp the oscillation.
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