Abstract
We consider systems of N bosons in $${\mathbb {R}}^3$$ , trapped by an external potential. The interaction is repulsive and has a scattering length of the order $$N^{-1}$$ (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum up to errors that vanish in the limit $$N\rightarrow \infty $$ .
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