  We introduce two possible ways of defining effective constraints of quantum
systems and applied this effective constraint method to models of WDW Quantum
Cosmology and Loop Quantum Cosmology. We analyze effective Hamiltonian
constraint on both second and third order and calculate Hubble parameter as
well as modified Friedmann equation of each model. Then we compare with a
special case using coherent state. It shows that this method is reasonable and
as before the classical Big Bang singularity is replaced by a quantum bounce in
Loop Quantum Cosmology.
