2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121640A Bethe-Ansatz spin-density functional approach is developed to evaluate the ground-state density profile in a system of repulsively interacting spin-1/2 fermions inside a quasi-one-dimensional harmonic well. The approach allows for the formation of antiferromagnetic quasi-order with increasing coupling strength and reproduces with high accuracy the exact solution that is available for the two-fermion system.3 pages, 2 figures, submittedStrongly Correlated Electronstext