Functional Change of Variables in the Wheeler--De Witt Equation

I present a new way to solve the Wheeler–de Witt equation using the invariance of the classical lagrangian under reparametrization. This property allows one to introduce an arbitrary function for each degree of freedom of the wave function $\mathrm{\Psi }$: this arbitrariness can be used to fix the asymptotic behaviour of $\mathrm{\Psi }$ so as to obtain a wave function representing a closed universe or a wormhole. These considerations are applied in detail to the Kantowsky–Sachs spacetime.