EXACT DIAGONALIZATION OF THE HAMILTONIAN FOR TRAPPED INTERACTING BOSONS IN LOWER DIMENSIONS

We consider systems of a small number of interacting bosons confined t o harmonic potentials in one and two dimensions. By exact numerical di agonalization of the many-body Hamiltonian we determine the low-lying excitation energies and the ground-state energy and density profile. W e discuss the dependence of these quantities on both interaction stren gth g and particle number N. The ground-state properties are compared to the predictions of the Gross-Pitaevskii equation, and the agreement is surprisingly good even for relatively low particle numbers. We als o calculate the specific heat based on the obtained energy spectra.