  In this paper, we show that there exists an essential difference of boundary
effects between Bose and Fermi systems both for Dirichlet and Neumann boundary
conditions: at low temperatures and high densities the influence of the
boundary on the Bose system depends on the temperature but is independent of
the density, but for the Fermi case the influence of the boundary is
independent of the temperature but depends on the density, after omitting the
negligible high-order corrections. We also show that at high temperatures and
low densities the difference of the influence of the boundary between Bose and
Fermi systems appears in the next-to-leading order boundary contribution, and
the leading boundary contribution is independent of the density. Moreover, for
calculating the boundary effects at high temperatures and low densities, since
the existence of the boundary modification causes the standard virial expansion
to be invalid, we introduce a modified virial expansion.
