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In this paper, we investigate the role of a high-frequency magnetic field inthe resonant behavior displayed by a spin-$1/2$ particle under the influence ofa rotating magnetic field. We propose two alternative methods for analyzing thesystem dynamics, namely, the averaging method and the multiple scale method.The analytical results achieved by applying these two methods are compared withthose obtained from the numerical solution of the Schr\"odinger equation. Thiscomparison leads to the conclusion that the multiple scale method provides abetter understanding of the system dynamics than the averaging method. Inparticular, the averaging method predicts the complete destruction of theresonant behavior by an appropriate choice of the parameter values of thehigh-frequency magnetic field. This conclusion is disproved both by thenumerical results, and also by the results obtained from the multiple scalemethod.

chemical physics

Effect of a high-frequency magnetic field on the resonant behavior  displayed by a spin-$1/2$ particle under the influence of a rotating magnetic  field