  We investigate the influence of a time dependent, homogeneous electric field
on scattering properties of non-interacting electrons in an arbitrary static
potential. We develop a method to calculate the (Keldysh) Green's function in
two complementary approaches. Starting from a plane wave basis, a formally
exact solution is given in terms of the inverse of a matrix containing
infinitely many 'photoblocks' which can be evaluated approximately by
truncation. In the exact eigenstate basis of the scattering potential, we
obtain a version of the Floquet state theory in the Green's functions language.
The formalism is checked for cases such as a simple model of a double barrier
in a strong electric field. Furthermore, an exact relation between the
inelastic scattering rate due to the microwave and the AC conductivity of the
system is derived which in particular holds near or at a metal-insulator
transition in disordered systems.
