FRW in cosmological self-creation theory: Hamiltonian approach

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $\rm[\frac{1}{\phi}(8\pi T^{\mu \nu (M)}+T^{\mu\nu (\phi)})]_{;\nu}=0$. We take as a first model the flat FRW metric in the Hamilton-Jacobi scheme and we present the Lagrange-Charpit approach in order to find classical solutions. In the quantum scheme, once we determine the characteristic surfaces, the quantum solution is obtained. These two classes of solutions are found for all values of the barotropic parameter $\gamma$.