We present a numerical scheme through which different phonon scattering processes can be incorporated into the quantum mechanical simulation of semiconductor devices. This method allows the effects of different phonon processes to be seen individually and without resorting to the use of fitting parameters to approximate the correct physics. We derive equations to include acoustic deformation potential scattering and intervalley phonon scattering accounting for both f- and g- type processes. Using this method we show that we are able to extract the correct mobility for bulk silicon at several different doping densities. The method is then applied to a gated silicon-on-insulator quantum wire device to illustrate the key deviations from the ballistic case that result from the inclusion of these two phonon scattering processes in quantum confined systems.