  We study ground state properties of spinless, quasi one-dimensional bosons
which are confined in a harmonic trap and interact via repulsive
delta-potentials. We use the exact diagonalization method to analyze the pair
correlation function, as well as the density, the momentum distribution,
different contributions to the energy and the population of single-particle
orbitals in the whole interaction regime. In particular, we are able to trace
the fascinating transition from bosonic to fermi-like behavior in
characteristic features of the momentum distribution which is accessible to
experiments. Our calculations yield quantitative measures for the interaction
strength limiting the mean-field regime on one side and the Tonks-Girardeau
regime on the other side of an intermediate regime.
