2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100500We present a formal derivation of the mean-field expansion for dilute Bose-Einstein condensates with two-particle interaction potentials which are weak and finite-range, but otherwise arbitrary. The expansion allows for a controlled investigation of the impact of microscopic interaction details (e.g., the scaling behavior) on the mean-field approach and the induced higher-order corrections beyond the s-wave scattering approximation.6 pages of RevTex4; extended discussion, added referencesOther Condensed Mattertext