The article presents a new interpretation of neutron scattering spectra by molecular systems that has much in common with the Franck-Condon theory describing the vibrational transitions in a molecule after absorption or emission of a photon. The principal elements are the quantum probabilities for the transitions between the energy levels of the studied system, which are induced by diffusion of a neutron. In this case, the fundamental concept of "energy landscapes", which was introduced by Hans Frauenfelder to describe the internal dynamics of proteins in terms of "jumps" between the minima of their (free) internal energy, can be integrated in the analysis of neutron scattering spectra by complex systems in general. The theory also provides an intuitive physical interpretation of Van Hove's correlation functions in the quantum regime, as well as their classical limit, which is usually considered in the analysis of quasi-elastic spectra of neutrons from proteins and other complex molecular systems.