both cases our technique allows to derive certain (strong) triangle inequalities involving the dispersions of (the logarithms of) the total volume and the scalar field momentum. The inequalities are general, valid for all the physical states admitted by the model. In the case $(i)$ they imply an exact preservation of the semiclassicality, whereas in $(ii)$ an analogous result is only partial, as it does not involve all the degrees of freedom describing the anisotropic system.

The treatment we introduce here is based on the observation, that the structure of the evolution operator in LQC implies that for each physical state (in certain sense) there exists the geometrodynamical (Wheeler-DeWitt) one, which is its large scale limit in either strict [@aps-imp; @posL] or approximate [@spher; @negL] sense. Furthermore in a large class of the models the structure of the physical Hilbert space of each geometrodynamical theory describing the limit admits a decomposition onto equivalents of Klein-Gordon plane waves either incoming from or outgoing to an infinite volume. Since the WDW limits of LQC states are formed out of “standing waves” coupling both the incoming and outgoing ones, one can perceive the LQC evolution as a scattering process, which transforms the WDW incoming 