  We employ the recently developed multi-time scale averaging method to study
the large time behavior of slowly changing (in time) Hamiltonians. We treat
some known cases in a new way, such as the Zener problem, and we give another
proof of the Adiabatic Theorem in the gapless case. We prove a new Uniform
Ergodic Theorem for slowly changing unitary operators. This theorem is then
used to derive the adiabatic theorem, do the scattering theory for such
Hamiltonians, and prove some classical propagation estimates and Asymptotic
Completeness.
