  The exact analytical solution of the degenerate Landau-Zener model, wherein
two bands of degenerate energies cross in time, is presented. The solution is
derived by using the Morris-Shore transformation, which reduces the fully
coupled system to a set of independent nondegenerate two-state systems and a
set of decoupled states. Due to the divergence of the phase of the off-diagonal
element of the propagator in the original Landau-Zener model, not all
transition probabilities exist for infinite time duration. In general, apart
from some special cases, only the transition probabilities between states
within the same degenerate set exist, but not between states of different sets.
An illustration is presented for the transition between the magnetic sublevels
of two atomic levels with total angular momenta J=2 and 1.
