  We obtain a time-dependent Schrodinger equation for the Friedmann - Robertson
- Walker (FRW) model interacting with a homogeneous scalar matter field. We
show that for this purpose it is necesary to include an additional action
invariant under the reparametrization of time. The last one does not change the
equations of motion of the system, but changes only the constraint which at the
quantum level becomes time-dependent Schrodinger equation. The same procedure
is applied to the supersymmetric case and the supersymmetric quantum
constraints are obtained, one of them is a square root of the Schrodinger
operator.
