An untraditional space-time method for describing the dynamics of high-field electron-hole wave packets in semiconductor quantum wells is presented. A finite-difference time-domain technique is found to be computationally efficient and can incorporate Coulomb, static, terahertz, and magnetic fields to all orders, and thus can be applied to study many areas of high-field semiconductor physics. Several electro-optical and electro-magneto-optical excitation schemes are studied, some well known and some new, and predicted observables are shown to be in qualitative agreement with experiment, where known.