  Equilibrium particle densities near a hard wall are studied for a quantum
fluid made of point charges which interact via Coulomb potential without any
regularization. In the framework of the grand-canonical ensemble, we use an
equivalence with a classical system of loops with random shapes, based on the
Feynman-Kac path-integral representation of the quantum Gibbs factor. After
systematic resummations of Coulomb divergences in the Mayer fugacity expansions
of loop densities, there appears a screened potential $\phi$. It obeys an
inhomogeneous Debye-H\"uckel equation with an effective screening length which
depends on the distance from the wall. The formal solution for $\phi$ can be
expanded in powers of the ratios of the de Broglie thermal wavelengths $\laa$'s
of each species $\alpha$ and the limit of the screening length far away from
the wall. In a regime of low degeneracy and weak coupling, exact analytical
density profiles are calculated at first order in two independent parameters.
Because of the vanishing of wave-functions close to the wall, density profiles
vanish gaussianly fast in the vicinity of the wall over distances $\laa$'s,
with an essential singularity in Planck constant $\hbar$. When species have
different masses, this effect is equivalent to the appearance of a quantum
surface charge localized on the wall and proportional to $\hbar$ at leading
order. Then, density profiles, as well as the electrostatic potential drop
created by the charge-density profile, also involve a term linear in $\hbar$
andwhich decays exponentially fast over the classical Debye screening length
$\xid$. The corresponding contribution to the global surface charge exactly
compensates the charge in the very vicinity of the surface, so that the net
electric field vanishes in the bulk, as it should.
