Asymptotic expansions general considerations

The consideration that the velocity of electrons is much higher than that of the nuclei (a consequence of their much smaller masses) leads to the Born-Oppenheimer approximation, perhaps the better known example of the near separability of variables. We reconsider it in view of subsequent generalizations. Using the language of classical mechanics, we will speak of adiabatic separability, which can be shown to be related to a semiclassical expansion, i.e. to an asymptotic expansion in h. See references [11-14] where we also discuss a post-adiabatic representation. 

---