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I am trying to grasp the difference between Raman scattering and fluorescence.
To me it appears that the former is described in a somewhat more classical context as ordinary inelastic scattering, while the latter actually has a meaningful quantum mechanical description.
So what is the quantum explanation for Raman scattering? I have read it involves a "virtual state" as an intermediate state. What is that supposed to mean?
If it just means (extremely) short lifetime, then there should be a mixed regime between Raman scattering and fluorescence, but I have never heard about that.
How does one calculate the virtual state if it "exists"?
This question is focused on the mathematics behind Raman scattering. How does one formulate Raman scattering of a photon and an atom, we may for simplicity assume that we have a hydrogen atom. e.g given some electronic state, how do I calculate the virtual states involved with Raman scattering?