  We derive a Magnus expansion for a frequency chirped quantum two-level
system. We obtain a time-independent effective Hamiltonian which generates a
stroboscopic time evolution. At lowest order the according dynamics is
identical to results from using a rotating wave approximation. We determine,
furthermore, also the next higher order corrections within our expansion scheme
in correspondence to the Bloch-Siegert shifts for harmonically driven systems.
Importantly, our scheme can be extended to more complicated systems, i.e. even
many-body systems.
