[en] The Drude Zener theory of the absorption of high frequency radiation by free carriers (inverse bremsstrahlung) has been extended into the quantum region (h-bar omega > k₀T) in terms of a frequency dependent relaxation time which predicts the dc mobility in the quasiclassical limit. Numerical calculations of the frequency and concentration dependent electron scattering rate have been completed for InP, InAs, Ga₀₄₇In₀₅₃As, and previous results for GaAs extended to high carrier concentrations. When starting from a quantum statistical theory, the fact that n/sub q/oh-bar omega → k₀T at low frequencies can be used to prevent the divergence of the coulomb scattering rate without inclusion of a screening radius. A result containing no adjustable parameters is found which predicts a mobility for uncompensated samples that decreases strongly at high concentrations. This has been observed in GaAs, and is not accounted for by the usual dc calculation which assumes h-bar omega = 0 and a screening parameter. Calculated results for GaAs are in good agreement with experimental measurements of the mobility which are found to be independent of a wide variety of conditions of material preparation. This indicates that disagreement with previous theoretical calculations was not due to compensation. Calculations for ZnSe and further investigation of the modification of the optical constants by the presence of an intense laser field and by a static magnetic field are currently planned