where c$_{1}$ , c$_{2}$ , c$_{1}$ ′ , c$_{2}$ ′ , c$_{1}$ ′′ and c$_{2}$ ′′ are normalisation coefficients. For the Hamiltonian operator to be self adjoint the wave function must satisfy one of the following boundary conditions [22], [23] The first boundary condition is satisfied while the second one leads to infinity. Obviously, the wave function is not square integrable and in order to obtain a possible physical solution we may construct wave packets as [23] However, the wave packets are also problematic and a satisfactory solution to the WDW equation is not easy to obtain. In the case of isotropic universe, the associated Wheeler-DeWitt equation, i.e., the Schr¨ odinger-like equation is The solution is where c$_{3}$ and c$_{4}$ are constants of integrations, J$_{+}$$_{ν}$ and J − ν are Bessel functions and ν = √$_{1}$ − 96 E/ 4. Since J − ν grows exponentially to infinity as a goes to zero, one must set c$_{4}$ = 0, and consequently the first boundary condition, (54), is satisfied. In this isotropic case the wave function is still not square integrable and even using wave packets does not give us a satisfactory wave function for the universe. In this work, we present the Hamiltonian formulation of the Bianchi type IX cosmological model minimally coupled to a scalar field. We show that the dynamics of the metric functions can be obtained using a time variable, T ( t ), as a function of the scalar field. 9 4. CONCLUSION Ψ$_{E}$( a, T ) = e − iET √$_{a}$ [ c$_{3}$J$_{+}$$_{ν}$ (3 a $^{2}$) + c$_{4}$J − $_{ν}$(3 a $^{2}$) ] , (58) − ∂ 2 $_{a}$Ψ − 36 a $^{2}$Ψ − i 24 a $_{2}$∂$_{T}$ Ψ = 0 . (57) ψ ( a, β$_{+}$, β − ; T ) = ∫ A ( E ) ψ$_{E}$ ( a, β$_{+}$, β − ; T ) dE. (56) Isotropic Bianchi type IX ψ ( a, β$_{+}$, β − , T ) | a =0 = 0 , (54) ∂ψ ( a, β$_{+}$, β − , T ) ∂a | a =0 = 0 . (55)