Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons

We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the ground state energy and density profile. We discuss the dependence of these quantities on both interaction strength g and particle number N. The ground state properties are compared to the predictions of the Gross-Pitaevskii equation, which depends on these parameters only through the combination Ng. We also calculate the specific heat based on the obtained energy spectra.