  We present an improved version of Berry's ansatz able to incorporate exactly
the existence of boundaries and the correct normalization of the eigenfunction
into an ensemble of random waves. We then reformulate the Random Wave
conjecture showing that in its new version it is a statement about the
universal nature of eigenfunction fluctuations in systems with chaotic
classical dynamics. The emergence of the universal results requires the use of
both semiclassical methods and a new expansion for a very old problem in
quantum statistical physics
