This research program will explore quantum dynamical processes for individual atoms strongly coupled to the field of an optical cavity. The research will include the investigation of the quantization of atomic center-of-mass motion within the setting of cavity quantum electrodynamics. Particular emphasis will be given to the dynamics of localized atomic wavepackets, both from the perspective of cooling and trapping single atoms with intracavity photon number of order unity and within the context of continuous quantum measurement. Results of this work have potential impact in the broad area of quantum computation, and partial support is provided by the Office of Multidisciplinary Activities (OMA).