Supporting random wave models: a quantum mechanical approach

We show how two-point correlation functions derived within non-isotropic random wave models are in fact quantum results that are obtained in the appropriate limit in terms of the exact Green function of the quantum system. Since no statistical model is required for this derivation, this shows that taking the wave functions as Gaussian processes is the only assumption of those random wave models. We also show how for clean systems the two-point correlation function defined through an energy average defines a Gaussian theory which substantially reduces the spurious contributions coming from the normalisation problem.