  We study nuclear propagation through avoided crossings of electron energy
levels. We construct a surface hopping semigroup, which gives an Egorov-type
description of the dynamics. The underlying time-dependent Schroedinger
equation has a two-by-two matrix-valued potential, whose eigenvalue surfaces
have an avoided crossing. Using microlocal normal forms reminiscent of the
Landau-Zener problem, we prove convergence to the true solution in the
semi-classical limit.
