A quantized closed Friedmann model

Dust-filled Friedmann universes have only one dynamical degree of freedom and one constraint (the Hamiltonian constraint), which plays the role of the generator of time evolution. In a corresponding quantum model the latter gives rise to a one-dimensional quantum mechanical wave equation. This equation is formulated in Ashtekar-type variables in two different factor orderings of the constraint operator, which turn out to require different Hilbert spaces. For each choice the spectra of the total mass and the maximal radius of the universe are discrete and for large quantum numbers both versions have acceptable classical limits.