  We show that, by means of a right-unitary transformation, the fully quantized
Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using
known solutions from the standard Landau-Zener problem. In the strong-coupling
regime, where the rotating wave approximation is not valid, we show that the
quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by
means of a unitary transformation; hence allowing numerical solutions for the
few photons regime via truncation.
