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What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not really looking for semiclassical approximations for time-independent Hamiltonian systems. Are there any modern reference-level texts/monographs or review articles that develop the mathematical theory and its applications for said models?

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Hi Christopher - book recommendations aren't really appropriate for Stack Exchange sites. We have some which are preserved from the early days of the site, listed in the book recommendation master thread, which you could have a look at. – David Z Apr 14 '13 at 22:56
I find that interpretation of the function of SE to be a little strange. In my opinion, the primary role of an academic forum should be to direct people to references or papers, especially when it comes to research-level subjects as in my case. – Christopher A. Wong Apr 14 '13 at 23:10
Hi Christopher, if you diagree with this recent change in policies, which disallows questions about any study material and references (papers), instigated by David Zaslavsky and a few other powerful people without the whole community having a saying about it, you should have a look at this meta thread and vote accordingly. There are some people who disagree with these new policies, but they are not powerful enough. Study material/reference questions should exactly be allowed for the site to be useful for students and researchers. – Dilaton Apr 14 '13 at 23:11
@DavidZaslavsky this is a research-level reference request questions, he is not specifically asking about books. Your enforcing of new policies which are not supported by the whole community is not right and now you are even shooting down research-level reference questions, this is definitively not cool. The original reference-request tag was right, I dont know why Qmechanic has exchanged it. – Dilaton Apr 14 '13 at 23:24
@Christopher perhaps so, but this is not an academic forum. It's a Q&A site, for focused, conceptual questions about physics. Recommendation questions and other similar questions which are only meant to accumulate lists don't work well here, so we don't allow them. – David Z Apr 14 '13 at 23:29

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