Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons
arXiv:cond-mat/9707107 · doi:10.1103/PhysRevA.57.3809
Abstract
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.
14 pages, 10 figures. The discussion on rescaling of the coupling is rewritten. Submitted to Phys. Rev. A
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