A Friedmann-Robertson-Walker universe filled with a conformally invari
ant scalar field is quantized by the reduced phase space method. In th
e gauge t = R, where R is the scale factor, a complete set of quantum
states is exhibited, whose properties are compared to those of the Har
tle-Hawking and Vilenkin wave functions. The issue of time, singularit
ies, and shortcomings of the current theories of initial conditions ar
e discussed.