Radiation-filled Friedmann-Robertson-Walker universes are quantized ac
cording to the Amowitt-Deser-Misner formalism in the conformal-time ga
uge. Unlike previous treatments of this problem, here both closed and
open models are studied, only square-integrable wave functions are all
owed, and the boundary conditions to ensure self-adjointness of the Ha
miltonian operator are consistent with the space of admissible wave fu
nctions. It turns out that the tunneling boundary condition on the uni
versal wave function is in conflict with self-adjointness of the Hamil
tonian. The evolution of wave packets obeying different boundary condi
tions is studied, and it is generally proven that all models are nonsi
ngular. Given an initial condition on the probability density under wh
ich the classical regime prevails, it is found that a closed universe
is certain to have an infinite radius, a density parameter Omega=1 bec
oming a prediction of the theory. Quantum stationary geometries are sh
own to exist for the closed universe model, but oscillating coherent s
tates are forbidden by the boundary conditions that enforce self-adjoi
ntness of the Hamiltonian operator. (C) 1996 American Institute of Phy
sics.