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A new class of solutions of the time-dependent Schrodinger equation is found for the two-state problem often encountered in quantum optics, magnetic resonance and atomic collisions. The authors use the Riemann-Papperitz differential equation to find exact solutions in terms of hypergeometric functions. They consider only cases in which the final occupation probabilities are elementary functions of the parameters of the model.
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Carroll et al. (1986) studied this question.
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