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

Closed-Orbit Theory of Spatial Density Oscillations in Finite Fermion Systems