Variational Calculations for the Spectrum of Finite Bosons inHarmonic Potentials

Using both the Gaussian and Fetter's variational calculations for the N-body ground-state wave function of the trapped Bose-Einstein condensate, we give explicit analytic formulas for the spectrum of finite bosons in harmonic potentials based on the corrected sum rules and generalized virial identities. We compare the low-lying excitation spectra among the Gaussian and Fetter's variational calculations and the exact numerical results. The Gaussian approximation has the simplest reasonable results, validing for N → ∞ and high-lying excitations.