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One-particle properties of non-interacting Fermions in a one-dimensionalharmonic trap and at zero temperature are studied. Exact expressions andasymptotic results for large Fermion number N are given for the particledensity distribution n_0(z,N). For large N and near the classical boundary atthe Fermi energy the density displays increasing fluctuations. A simple scalingof these tails of the density distribution with respect to N is established.The Fourier transform of the density distribution is calculated exactly. Itdisplays a small but characteristic hump near 2 k_F with k_F being a properlydefined Fermi wave number. This is due to Friedel oscillations which areidentified and discussed. These quantum effects are missing in thesemi-classical approximation. Momentum distributions are also evaluated anddiscussed. As an example of a time-dependent one-particle problem we calculateexactly the evolution of the particle density when the trap is suddenlyswitched off and find a simple scaling behaviour in agreement with recentgeneral results.Comment: to appear in Phys.Rev.A, RevTex, 10 pages with 3 eps-figures, gzipped  tar-fil

Noninteracting fermions in a one-dimensional harmonic atom trap: Exact one-particle properties at zero temperature