# Necessary and suficient conditions for Scattering to be Elastic

Pretty straightforward: what basic assumptions must we make in constructing a Scattering Theory, in Quantum Mechanics, in order for it to conserve energy of the incident particle (i.e. to be elastic)?

My gut tells me it has to do with Hamiltonian being time-independent or maybe time-reversal symmetric. Is this the right path? If so, how could I go to formalize this ideas?