  Wormhole boundary conditions for the Wheeler--DeWitt equation can be derived
from the path integral formulation. It is proposed that the wormhole wave
function must be square integrable in the maximal analytic extension of
minisuperspace. Quantum wormholes can be invested with a Hilbert space
structure, the inner product being naturally induced by the minisuperspace
metric, in which the Wheeler--DeWitt operator is essentially self--adjoint.
This provides us with a kind of probabilistic interpretation. In particular,
giant wormholes will give extremely small contributions to any wormhole state.
We also study the whole spectrum of the Wheeler--DeWitt operator and its role
in the calculation of Green's functions and effective low energy interactions.
