ABSTRACT
This chapter is really the heart and soul of this text-not only in a physical sense but also in a scientific sense. In the early days of quantum mechanics and especially chemical physics, we were mostly interested in discerning the energy states or predicting equilibrium structures of a given atomic or molecular system. This provided a good test of quantum theory and deepened our understanding of the nature of the bonding and intermolecular interactions that define a chemical system. With the introduction of time-resolved laser techniques in the 1980s, modern investigations have focused upon pulling apart how an atomic or molecular system undergoes transitions from one state to the next and how the quantum interferences between different pathways influence these transitions. Typically, in a molecular system we treat the electronic degrees of freedom using rigorous quantum theory and allow their energies and states to be parametrized by the instantaneous positions of the nuclei. This is justified through the Born-Oppenheimer approximation, which allows us to separate the fast motion of the electrons from the far slower motions of the nuclei by virtue of their disparity in mass. As we shall see in this chapter, things become interesting when the separation of time scales is no longer valid.
