  Friedel oscillations appear in density of Fermi gases due to Pauli exclusion
principle and translational symmetry breaking nearby a defect or impurity. In
confined Fermi gases, this symmetry breaking occurs also near to boundaries.
Here, density oscillations of a degenerate and confined Fermi gas are
considered and characterized. True nature of density oscillations are
represented by analytical formulas for degenerate conditions. Analytical
characterization is first done for completely degenerate case, then temperature
effects are also incorporated with a finer approximation. Envelope functions
defining the upper and lower bounds of these oscillations are determined. It is
shown that the errors of obtained expressions are negligible as long as the
system is degenerate. Numbers, amplitudes, averages and spatial coordinates of
oscillations are also given by analytical expressions. The results may be
helpful to efficiently predict and easily calculate the oscillations in density
and density-dependent properties of confined electrons at nanoscale.
