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 kine tic pressure profiles in inhomogeneous one-dimensional systems of nonintera cting fermions, and apply it to harmonically confined systems of up to N = 1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calcula tion of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi approximation, the exact pr ofiles show negative local pressure in the tails and a prominent shell stru cture which may become accessible to observation in magnetically trapped ga ses of fermionic alkali atoms.