Quantum cosmological backreactions. II. Purely homogeneous quantum cosmology

In this second paper in a series of four, we continue with the program incorporating backreaction among homogeneous and between inhomogeneous degrees freedom quantum cosmological perturbation theory. The purpose present is to illustrate formalism space adiabatic theory for two simple mechanical models, prove that indeed leads additional correction terms effective Hamiltonians one would otherwise neglect crude Born-Oppenheimer approximation. first model consists harmonic oscillator coupled an anharmonic oscillator. describes coupling scalar matter field gravity restricted purely isotropic sector. These results have potential phenomenological consequences models.