One - parameter family of closed , radiation - filled Friedmann - Robertson - Walker “ quantum ” universes

Using as an illustrative example the p=1 operator-ordered Wheeler-DeWitt equation for a closed, radiation-filled Friedmann-Robertson-Walker universe, we introduce and discuss the supersymmetric double Darboux method in quantum cosmology. A one-parameter family of " quantum " universes and the corresponding " wavefunctions of the universe " for this case are presented. Many interesting results have been obtained mostly in one-dimensional quantum mechanics by means of Darboux-Witten (DW) supersymmetric procedures; for a recent review see [1]. These are, essentially, factorizations of the one-dimensional Schrödinger differential operator, first performed in the supersymmetric context by Witten in 1981 [2], and in mathematics literature , in the broader sense of the Darboux transformation, by Darboux, as early as 1882 [3]. Constructing families of isospectral potentials is an important supersymmetric topic which may