  A quantum cosmological bouncing model may exhibit an ambiguity stemming from
the nonclassical nature of the background evolution: two classically equivalent
theories can produce two qualitatively different potentials sourcing the
perturbations. We derive explicitly the quantum canonical transformation
involving the quantum background to show how it leads to inequivalent theories.
We identify the relevant quantum parameter describing the difference and expand
upon the ambiguity by calculating the expected power spectra produced for
initial quantum vacuum fluctuations in the contracting phase of both
potentials. We find that one spectral index corresponds to all values of this
parameter but one, while the other thus represents a set of measure zero.
