  We present two different approaches towards the Landau-Zener problem: (i) The
Markov approximation in the integro-differential equation for one of the two
probability amplitudes, and (ii) an amplitude-and-phase analysis of the linear
second order differential equation for same probability amplitude. Our
treatment shows that the Markov approximation neglects the non-linearity of the
equation but still provides us with the exact asymptotic result.
