A spectroscopic interpretation of incoherent neutron scattering experiments is presented which is based on Franck–Condon-type probabilities for scattering-induced transitions between quantum states of the target. The resulting expressions for the scattering functions enable an energy landscape-oriented analysis of neutron scattering spectra as well as a physical interpretation of Van Hove’s space–time correlation functions in the quantum regime that accounts for the scattering kinematics. They suggest moreover a combined analysis of quasi- and inelastic scattering that becomes inseparable for complex systems with slow power-law relaxation.