  We discuss how to fix the gauge in the canonical treatment of Lagrangians,
with finite number of degrees of freedom, endowed with time reparametrization
invariance. The motion can then 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 \S equation for the on--shell
wave function (Presented at the International Workshop ``Birth of the Universe
and Fundamental Physics'', Rome, May 18-21, 1994).
