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This thesis work is on the theoretical description of dilute Bose-Einstein condensates (BEC) that are non-uniform, meaning that more than one single-particle state is occupied. This phenomenon is usually called quantum depletion. A common model for the ground state of a dilute and weakly interacting BEC is the mean-field (MF) approximation leading to the Gross-Pitaevskii (GP) equation. However, fo
