The exact quantum dynamics of a single spin-1/2 in a generic time-dependent classical magnetic field are investigated and compared with the quantum motion of a spin-1/2 studied by Rabi and Schwinger. The possibility of regarding the scenario studied here as a generalization of that considered by Rabi and Schwinger is discussed and the notion of a time-dependent resonance condition is introduced and carefully legitimated and analyzed. Several examples help to disclose analogies and departures of the quantum motion induced in a generalized Rabi system with respect to that exhibited by the spin-1/2 in a magnetic field precessing around the z-axis. It is found that, under a generalized resonance condition, the time evolution of the transition probability (Formula presented.) between the two eigenstates of (Formula presented.) may be dominated by a regime of distorted oscillations, or may even exhibit a monotonic behavior. At the same time, the authors succeed in predicting asymptotic behaviors with no oscillations in the time-dependence of (Formula presented.) under general conditions. New scenarios of experimental interest originating a Landau–Zener transition are brought to light.
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