Probability space of wave functions

It is well known that in quantum mechanics, when the mean value of an observable is given, entropy maximization (von Neumann, Born, Jaynes) can be successfully applied for constructing a probability distribution on the set of possible values of that observable. In this paper, the entropy maximization technique is extended to the complex domain in order to construct an unbiased probability measure on the set of all wave functions. In particular, a justification and a generalization of the Wiener-Siegel probability distribution of Gaussian type in the differential space of wave functions are given.