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We consider systems of a small number of interacting bosons confined toharmonic potentials in one and two dimensions. By exact numericaldiagonalization of the many-body Hamiltonian we determine the low lyingexcitation energies and the ground state energy and density profile. We discussthe dependence of these quantities on both interaction strength g and particlenumber N. The ground state properties are compared to the predictions of theGross-Pitaevskii equation, which depends on these parameters only through thecombination Ng. We also calculate the specific heat based on the obtainedenergy spectra.Comment: 14 pages, 10 figures. The discussion on rescaling of the coupling is  rewritten. Submitted to Phys. Rev.

Exact diagonalization of the Hamiltonian for trapped interacting bosons in lower dimensions