T. Haugset et H. Haugerud, EXACT DIAGONALIZATION OF THE HAMILTONIAN FOR TRAPPED INTERACTING BOSONS IN LOWER DIMENSIONS, Physical review. A, 57(5), 1998, pp. 3809-3817
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.