= Solution
On Rabi resonance, $\omega=\omega_0$ and $\Omega=0$, so
$$
\boxed{P_-(t)=|c_2(t)|^2=\sin^2(\gamma t).}
$$
For nonzero drive the <probability> starts at zero, reaches unity at $t=\pi/(2|\gamma|)$, and repeats with <period> $\pi/|\gamma|$. The population oscillation therefore has <angular frequency> $2|\gamma|$. This is complete resonant Rabi transfer; a drive of zero strength gives no transition.
\Image[/past-exam-of-the-quantum-physics-course-of-the-university-of-oxford/2016-resonant-and-detuned-spin-oscillations.png]
{title=Resonant and detuned spin transition probabilities}
{description=The dimensionless time is the drive coupling times time. The detuned example uses half-detuning equal to the drive coupling, making the maximum transition probability one half.}
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