Abstract
We consider the motion of a single electron under phonon scattering caused by a crystal lattice. Starting from the Fröhlich Hamiltonian in the second quantization formalism we derive a kinetic transport model by using the Wigner transformation. Under the assumption of small electron-phonon interaction we derive asymptotically the operator representing electron-phonon scattering in the Wigner equation. We then consider some scaling limits and finally we give the connection of our result to the well known Barker-Ferry equation.