  We investigate the particle and kinetic-energy densities for $N$
non-interacting fermions confined in a local potential. Using Gutzwiller's
semi-classical Green function, we describe the oscillating parts of the
densities in terms of closed non-periodic classical orbits. We derive universal
relations between the oscillating parts of the densities for potentials with
spherical symmetry in arbitrary dimensions, and a ``local virial theorem''
valid also for arbitrary non-integrable potentials. We give simple analytical
formulae for the density oscillations in a one-dimensional potential.
