  We study the quantum cosmology of a flat
Friedmann-Lema\^{i}tre-Robertson-Walker universe filled with a (free) massless
scalar field and a perfect fluid that represents radiation or a cosmological
constant whose value is not fixed by the action, as in unimodular gravity. We
study two versions of the quantum theory: the first is based on a time
coordinate conjugate to the radiation/dark energy matter component, i.e.,
conformal time (for radiation) or unimodular time. As shown by Gryb and
Th\'ebault, this quantum theory achieves a type of singularity resolution; we
illustrate this and other properties of this theory. The theory is then
contrasted with a second type of quantisation in which the logarithm of the
scale factor serves as time, which has been studied in the context of the
"perfect bounce" for quantum cosmology. Unlike the first quantum theory, the
second one contains semiclassical states that follow classical trajectories and
evolve into the singularity without obstruction, thus showing no singularity
resolution. We discuss how a complex scale factor best describes the
semiclassical dynamics. This cosmological model serves as an illustration of
the problem of time in quantum cosmology.
