Exact Particle and Kinetic-Energy Densities for One-Dimensional Confined Gases of Noninteracting Fermions

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of noninteracting fermions, and apply it to harmonically confined systems of up to $N=1000\mathrm{}$ fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi approximation, the exact profiles show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.