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I happened to have need for a stub Born-Oppenheimer approximation
I think that in the abstract form (at least in the generality I was doing research when working on a project in physical chemistry) Born-Oppenheimer approximation is about the distinction between fast changing and slow changing degrees of freedom; there is perturbation theory associated to the decomposition of the Hilbert space into products (that is we have a tensor product decomposition of the Hilbert space). The fact that the motion of heavy particles and light particles in a system is a special case of that is not essential for general statement of the problem. One has to write a general form of Hamiltonian which corresponds to the interpretation which makes plausible the perturbation theory in which the slowliness of some degrees of freedom is capitalized on. I do not have my notes with me, but I think it is not to difficult to recnstruct he general framework.
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