In compound semiconductor crystals with a substantial degree of ionicity Froelich interaction of charge carriers with longitudinal optical (LO) phonons is strong enough to produce detectable polaron effects. In this paper polaron effects are analysed using a quantum theory of electron transport based on the momentum- and frequency-dependent Wigner function fw(p, ohgr), defined starting from the G< Green function, simply related to the electron spectral function A(p, ohgr). The theoretical approach considers the dynamical evolution of the electron Wigner function in the presence of phonon scattering. An elaboration of the quantum dynamical equation in terms of Wigner paths formed by free flights and scattering events is used. These paths are especially suitable for a Monte Carlo solution of the transport equation for the Wigner function very similar to the semiclassical traditional Monte Carlo solution of the Boltzmann equation. Numerical results for GaAs and CdTe in a variety of physical conditions are presented.