The Born-Oppenheimer approximation is first and foremost a simplification of the equations following from the time independent Schroedinger equation. The author

The Born-Oppenheimer approximation is first and foremost a simplification of the equations following from the time independent Schroedinger equation. The author probably wanted to stress the fact that this simplification does not follow from any other general principle of quantum theory but is necessary to use it in order to make use of the Schr. equation in chemistry (most theory of molecules is based on this approximation). If we do not make the approximation, the equations are complex and we cannot derive the usual results of quantum chemistry.