  We develop an action principle for those models arising from isotropic loop
quantum cosmology, and show that there is a natural conserved quantity $Q$ for
the discrete difference equation arising from the Hamiltonian constraint. This
quantity $Q$ relates the semi-classical limit of the wavefunction at large
values of the spatial volume, but opposite triad orientations. Moreover, there
is a similar quantity for generic difference equations of one parameter arising
from a self-adjoint operator.
