Noncondensate atoms in a trapped Bose gas

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Abstract
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.