Scattering has a very general meaning. Any type of collision can be called a scattering. Another example of scattering is the reflection of light on a mirror, in which case the light (more accurately, the photons) is scattered. In the most general sense, any change of state can be considered as a scattering.

Scatterings can be treated using either classical mechanics or quantum mechanics, depending on the size of the scattering objects. In scattering, the momentum of the system is always conserved. This can be derived easily using Newton's third law in classical mechanics. In the microscopic world where we must use quantum mechanics, there are subtle issues because of the uncertainty principle. The momentum of the system long before and long after the scattering is always equal. "Long" means that the period of time is large compared with the scattering time.

The energy of the system is...