Norm convergence of confined fermionic systems at zero temperature

The semi-classical limit of ground states of large systems of fermions was studied by Fournais, Lewin and Solovej in (Calc. Var. Partial Differ. Equ., 2018). In particular, the authors prove weak convergence towards classical states associated to the minimizers of the Thomas-Fermi functional. In this paper, we revisit this limit, and show that under certain assumptions–and, using simple arguments–it is possible to prove that strong convergence holds true in relevant normed spaces.