We discuss how to fix the gauge in the canonical treatment of Lagrangi
ans, with a finite number of degrees of freedom, endowed with time rep
arametrization invariance. The motion can be described by an effective
Hamiltonian acting on the gauge shell canonical space. The system is
then suited for quantization. We apply this treatment to the case of a
Robertson-Walker metric interacting with zero modes of bosonic fields
and write a Schrodinger equation for the on-shell wave function.