  The Euclidean quantum amplitude to go between data specified on an initial
and a final hypersurface may be approximated by the tree amplitude
exp(-I_{classical}/\hbar), where I_{classical} is the Euclidean action of the
classical solution joining the initial and final data. In certain cases the
tree amplitude is exact. We study I_{classical} hence the quantum amplitude, in
the case of a spherically symmetric Riemannian gravitational field coupled to a
spherically symmetric scalar field. The classical scalar field obeys an
elliptic equation, which we solve using relaxation techniques, in conjunction
with the field equations giving the gravitational field. An example of the
transition from linearity to non-linearity is presented and power law behavior
of the action is demonstrated.
