  New fluctuation properties arise in problems where both spatial integration
and energy summation are necessary ingredients. The quintessential example is
given by the short-range approximation to the first order ground state
contribution of the residual Coulomb interaction. The dominant features come
from the region near the boundary where there is an interplay between Friedel
oscillations and fluctuations in the eigenstates. Quite naturally, the
fluctuation scale is significantly enhanced for Neumann boundary conditions as
compared to Dirichlet. Elements missing from random plane wave modeling of
chaotic eigenstates lead surprisingly to significant errors, which can be
corrected within a purely semiclassical approach.
