Gaussian random eigenfunctions and spatial correlations in quantum dots

We show that spatial correlations in wave functions of quantum dots, obtained earlier by averaging over a random potential via supermatrix techniques can be computed with much less effort by making use of Berry's conjecture that the energy eigenfunction in a quantized chaotic system are Gaussian random variables. Furthermore, in the case of a time-reversal invariant system, we find a greatly simplified (though equivalent) formula for these correlations.