Boundary conditions and the cosmological constant

We consider various simplified models of quantum gravity in which we propose a method for determining the boundary conditions for the cosmological wave functions. The basic idea is to require a set of operators, chosen on physical grounds, to be observables; the boundary conditions thus implied are seen to be the ones used previously by DeWitt and to differ little from the ones proposed by Hartle and Hawking. We further note that, in certain regions of parameter space, such boundary conditions can be implemented only if a quantization condition is imposed upon the cosmological constant.