For all but the simplest models for the electronic potentials, one must resort to a numerical calculation of the observed spectrum. There are a number of interesting models which are simple enough to determine the wavefunctions yet to complicated to work out the theoretical spectra by hand. This project also has application to the vibrational spectra of molecules in the condensed phase. This project will give you experience with and important topic in physical chemistry and also with Mathematica . If you are interested in a project along these lines please stop by and talk to me about it.
Spectroscopy involves the interaction of light with matter.
From this interaction one is able to gain a wealth of information about the molecular structure and dynamics of material samples. Ultrafast molecular events are also central to understanding photo-initiated chemical reactions and to the exciting prospect of controlling such reactions with tailored optical fields. Any random process is characterized by a correlation time which is inversely proportional to the degree of randomness or noise. This ultrashort noise correlation time offers the time resolution to measure ultrafast molecular dynamics. It is believed that the set of FTC diagrams represents the decomposition of any given noisy light-based nonlinear spectroscopy into its most elementary 'physically' meaningful components.