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Like, when I think "scattering" I imagine little balls hitting each other and being repelled backwards, but obviously that's not really what happens with, e.g., Compton scattering, because electrons and protons and other so-called particles aren't little solid balls. Of course, they aren't really classical waves either, but they're much closer to classical waves than anything else in classical physics, at least in the math of QM. But in that case, what does it even mean for particles to scatter?

I have a basic understanding of Compton scattering in particular, but I don't get why it's called "scattering" at all -- what's being scattered? Isn't it all about photons losing energy by interacting with electrons, and so their wavelength increases?

I did Google variations of "wave scattering" and "scattering in quantum mechanics" and I found plenty of stuff talking about it, but it all seems completely different from the classical notion of scattering. In fact, it seems like nothing more or less than wave interference causing a net change in direction -- is it just the change in direction that qualifies a wave interaction as "scattering" rather than just generic wave interference?

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You start with some particles of pretty-well-defined momentum. Some interaction happens in between, which may be not fully understood in a time-dependent way but enough to get results for this type of experiment: in scattering experiments we look for the results only as $t \to \infty$. The process ends by measuring the momentum of whatever comes out, after waiting enough time during which the outgoing particles aren't subjected to an interaction that would obfuscate the results - sometimes the particles are free but they may for example be in a magnetic field. Predicting the outcome of these experiments (usually in terms of the differential scattering cross section, though in principle it can equivalently just be by predicting the distribution of different final momenta) is to predict the results of a scattering experiment. Anything which can fit this mould is considered a scattering experiment.

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  • $\begingroup$ Not only particles. It also applies to classical waves with a precise frequency and wavelength that encounter some obstacle. $\endgroup$
    – Mauricio
    Feb 21, 2023 at 23:32

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