ABSTRACT
This chapter focuses on a unified theoretical treatment of collisions and spectroscopy using the concept of the auto-correlation function with a natural link to signal processing. The concept of auto-correlation functions emerged as a computational tool, but soon afterwards surpassed its initial purpose. This is because the auto-correlation functions represent a veritable alternative formulation of quantum mechanics and quantum-mechanical resonant scattering theory. Many of the major observables, e.g. complete energy spectra, local density of states, quantal rate constants and other related quantities are expressible through auto-correlation functions or their suitable transforms. Other important observables could be given completely in terms of some appropriate, relatively small informational parts that might be singled out and analysed separately from the unwanted/redundant remainder of the full data set of autocorrelation functions. To theoretically generate auto-correlation functions, that play a critical role in analysis of spectra of physical systems, all the parametric methods require that the peak parameters are computed as pairs of complex numbers.
