ABSTRACT
This chapter examines the calculation of state-to-state transition probabilities between the states of harmonic oscillators under time-dependent perturbations. It discusses the symmetry of the matrix elements with respect to the permutation of their subscripts. When there are insufficient laboratory data to make more elaborate calculations, or in model studies of the systematics of arrays of Franck- Condon factors, it is customary to consider harmonic oscillations in both electronic states. The calculation of Franck-Condon factors within the harmonic approximation is so easy that many authors have developed their own formulas for the vibrational overlaps, some of which are widely applied to the interpretation of electronic spectra. However, one should conduct such application carefully because the harmonic approximation is so crude that the resulting Franck-Condon factors exhibit an unwanted and puzzling feature: the transpose array is in better agreement with the experimental spectral intensities than the array itself.
