12.1: A Classical Description of Spectroscopy The traditional quantum mechanical treatment of spectroscopy is a static representation of a very dynamic process. An oscillating light field acts to drive bound charges in matter, which under resonance conditions leads to efficient exchange of energy between the light and matter. This dynamical picture emerges from a time-domain description, which shares many similarities to a classical description. 12.2: Time-Correlation Function Description of Absorption Lineshape A time-correlation function for the dipole operator can be used to describe the dynamics of an equilibrium ensemble that dictate an absorption spectrum. We will make use of the transition rate expressions from first-order perturbation theory that we derived in the previous section to express the absorption of radiation by dipoles as a correlation function in the dipole operator. L 12.3: Different Types of Spectroscopy Emerge from the Dipole Operator The absorption spectrum in any frequency region is given by the Fourier transform over the dipole correlation function that describes the time-evolving change distributions in molecules, solids, and nanosystems. Let’s consider how this manifests itself in a few different spectroscopies, which have different contributions to the dipole operator. 12.4: Ensemble Averaging and Line-Broadening There are numerous processes that can influence the lineshape. These can be separated by dynamic processes intrinsic to the molecular system, which is termed homogeneous broadening, and static effects known as inhomogeneous broadening, which can be considered an ensemble averaging effect.