 Solution

The populations giveTogether with $⟨S_y⟩=(\hslash /2)\sin (\Omega t)$, 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 $d⟨\mathbf{S}⟩/dt=\gamma ⟨\mathbf{S}⟩\times \mathbf{B}$. 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.