Employing the Feynman procedure of ordered exponential operators and the stationary phase method to evaluate the multiple integrals involved, we calculate the level-crossing probability and analyze the role of a resonance in the evolution of a two-level neutrino system. We compare this procedure with more conventional ones, such as Landau's method and the ansatz of Kuo and Pantaleone and Petcov. We verify that our results reproduce the correct extreme nonadiabatic limit and give the standard

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... utions in the adiabatic regime for any arbitrary matter density distributions. We discuss in particular the case of solar neutrino propagation using the standard solar model predictions for the matter distribution in the Sun. PACS number(s): 14.60. Pq, 96.60.Kx