ABSTRACT
This chapter presents the mathematical structure necessary to describe the experimental results. It aims to develop analytic models describing the dynamics, as well as the tools needed for numerical simulations. Since time-resolved spectroscopy experiments involve applied electromagnetic fields, developing our understanding of field-driven dynamics is clearly important as well. Interpreting experimental results is nontrivial, and typically requires a mathematical structure that parallels the physical apparatus used to carry out the experiment. The chapter explores the basic mathematical background of field-driven dynamics. For experiments measuring coherent emission of light from a molecular ensemble, it is useful to calculate the microscopic polarization of the molecules after interaction with both pump and probe pulses. This can then be used to determine the macroscopic polarization and resulting field that propagates according to Maxwell’s equations in conjunction with the time-dependent Schrödinger equation.
