ISAACSON EXPANSION IN QUANTUM COSMOLOGY

This paper is an application of the ideas of the Born-Oppenheimer (or slow-fast) approximation in molecular physics and of the Isaacson (or short-wave) approximation in classical gravity to the canonical quanti zation of a perturbed minisuperspace model of the kind examined by Hal liwell and Hawking. Its aim is the clarification of the role of the se miclassical approximation and back reaction in such a model. The Isaac son approximation to the quantum model, although it includes the semic lassical approximation, and requires the solution of something resembl ing a time-dependent Schrodinger equation, has solutions which are not semiclassical, and semiclassical solutions in which the quantum pertu rbations are highly excited.