Abstract
From the asymptotic expansion of the ground state of the Gross–Pitaevskii equation in the Thomas–Fermi limit given by Gallo and Pelinovsky [“On the Thomas-Fermi ground state in a harmonic potential,” Asymptot. Anal. 73(1–2), 53–96 (2011)]10.3233/ASY-2011-1034, we infer an asymptotic expansion of the kinetic, potential, and total energy of the ground state. In particular, we give a rigorous proof of the expansion of the kinetic energy calculated by Dalfovo, Pitaevskii, and Stringari [“Order parameter at the boundary of a trapped Bose gas,” Phys. Rev. A 54, 4213–4217 (1996)]10.1103/PhysRevA.54.4213 in the case where the space dimension is 3. Moreover, we calculate one more term in this expansion, and we generalize the result to space dimensions 1 and 2.
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