The Riccati equation bridges the two probability amplitudes in Landau-Zener transitions and pinpoints why the Markov approximation succeeds for one amplitude but fails for the other.
(26), for the probability amplitude a introducing the function η which leads us directly to the non-linear differential equation of first order, eq
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Hidden facts in Landau-Zener transitions revealed by the Riccati Equation
The Riccati equation bridges the two probability amplitudes in Landau-Zener transitions and pinpoints why the Markov approximation succeeds for one amplitude but fails for the other.