We formulate Bogoliubov theory for a weakly interacting Bose-Einstein condensate confined to a spherically symmetric harmonic-oscillator potential. The theory is solved numerically by diagonalizing a Hamiltonian that is second order in boson creation and annihilation operators with the aid of a symplectic transformation. At zero temperature, the number of noncondensate atoms is well approximated by a heuristic expression based on Bogoliubov theory for free atoms.

• Received 8 July 1996

DOI:https://doi.org/10.1103/PhysRevA.54.R3722