nLab Born-Oppenheimer approximation

Idea

In quantum mechanics, the Born–Oppenheimer approximation is a method for approximating the energy a quantum mechanical system by identifying “light” and “heavy” degrees of freedom and then treating the solving for the “light” dynamics as if depending only on the static configuration of the “heavy” degrees of freedom.

Historically this is motivated from, and still heavily used in practice, for the computation of energy spectra of molecules, where the atomic nuclei are much heavier than the electrons, so that their dynamics can be split off to a good degree of approximation.

References

The original reference is

• Max Born, Robert Oppenheimer, Zur Quantentheorie der Molekeln, Annalen der Physik. 389, Nr. 20 (1927), p 457–484, doi:10.1002/andp.19273892002.

An early textbook-like account is

• J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 1: Electronic Structure of Molecules American Journal of Physics. 32, (1964), S. 65, doi:10.1119/1.1970097.

An review is for instance in section 2.2 The Born-Oppenheimer approximation of

• Peter David Haynes, Linear-scaling methods in ab initio quantum-mechanical calculations PhD thesis (1998) (web)