  We study the Bose-Einstein condensates of trapped Bose gases in the
Gross-Pitaevskii regime. We show that the ground state energy and ground states
of the many-body quantum system are correctly described by the Gross-Pitaevskii
equation in the large particle number limit, and provide the optimal
convergence rate. Our work extends the previous results of Lieb, Seiringer and
Yngvason on the leading order convergence, and of Boccato, Brennecke,
Cenatiempo and Schlein on the homogeneous gas. Our method relies on the idea of
'completing the square', inspired by recent works of Brietzke, Fournais and
Solovej on the Lee-Huang-Yang formula, and a general estimate for Bogoliubov
quadratic Hamiltonians on Fock space.
