On the mathematical treatment of the Born-Oppenheimer approximation.
Résumé
Motivated by a paper by B.T. Sutcliffe and R.G. Woolley, we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of rigourous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The paper neither contains mathematical statements nor proofs. Instead we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.
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