ABSTRACT
Quantum systems whose dynamics depends on one or more control functions are called quantum control systems. This chapter describes elements of the theory of field-particle interaction. It starts with the classical theory of electrodynamics and shows how to obtain the quantum mechanical description through a process called canonical quantization. The chapter presents physical examples of quantum control systems of interest in applications and highlights the fact that such systems have a common mathematical structure. In the external system, the motion of the charges, are fixed and independent of the field. Canonical quantization is the process which associates quantities in classical mechanics with operators in quantum mechanics.
