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This question already has an answer here:

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?

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marked as duplicate by Rococo, ZeroTheHero, Jon Custer, Yashas, sammy gerbil Mar 29 '17 at 4:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ You also may be interested in: physics.stackexchange.com/questions/184261/… $\endgroup$ – Rococo Mar 28 '17 at 16:43
  • $\begingroup$ @Rococo Both references only slightly touch the topic and do not really give solid answers. $\endgroup$ – iolo Mar 28 '17 at 19:34
  • $\begingroup$ okay, I will try to give an answer later if I get the chance $\endgroup$ – Rococo Mar 28 '17 at 21:39
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    $\begingroup$ Raman certainly has explicit quantum mechanical descriptions. The interaction of a photon with a phonon in a solid is described in any number of textbooks. Could you perhaps clarify the issue? $\endgroup$ – Jon Custer Mar 29 '17 at 2:30
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    $\begingroup$ Only the last part of your original question (v1) mentions calculation. If the mathematics of Raman scattering is your focus then I think you should edit again to remove the other questions and also show some mathematics to explain exactly what part of it you do not understand. $\endgroup$ – sammy gerbil Mar 29 '17 at 16:59
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The main difference between the two is the time scale, as you've already discussed a bit in your question. The other main Physical difference is that fluorescence is the result of relaxation from an electronic state, whereas Raman scattering is the result of relaxation from vibrational states.

A virtual state is a shortlived state that can't be described particularly well, you can't define its occupation for example. You can however define a lifetime for them using the uncertainty relations, which I'm guessing is what the source of the short timescales involved in Raman scattering.

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  • $\begingroup$ I like your answer, but it is not very detailed. Could you perhaps add some references? $\endgroup$ – iolo Mar 28 '17 at 19:33
  • $\begingroup$ I'm only jsut getting to grips with this myself so this is for the most part what I've learned from the wikipedia page for Raman Scattering. It even has a subsection that discusses your exact question, mentioning a detail that I forgot in my previous comment that Raman scattering is wavelength independent (i.e. the excitation does not need to be a particular frequency), whereas flourescence requires the incident photons to be resonant with the relevant transition. $\endgroup$ – kw111 Mar 28 '17 at 20:40

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