Perhaps this question is silly, but I don't entirely understand how elastic scattering of photons is even possible given that the directions of the incident/scattered photon differ. If there is a change in direction of the photons momentum, then there must be some momentum transferred to the scattering atom, hence the scattered photon should have less energy than the incident photon (which is not elastic scattering). The only way I could see elastic scattering make sense is if the nucleus mass is large enough so that the nucleus recoil is negligible (which is analogous to a ball bouncing off of a wall of infinite mass), but I find this hard to believe since moving atoms using photons is the basis of laser cooling. Another possible explanation is that the energy of the scattered photon *is* decreased, but the decrease is within the linewidth of photon energy distribution (..or something--this is a very iffy argument). Anyway, any help would be great. This question came up when talking about Rayleigh scattering, and I actually don't exactly understand how that works either from a quantum standpoint (i.e., not modelling light as a wave which drives a dipole).