In this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground-state energy of the relative motion of a system of two fermions with spin up and spin down interacting via a delta-function potential in a one-dimensional (1D) harmonic trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.
Physical review. A, Atomic, molecular, and optical physics. New York. Vol. 86, no. 4 (Oct. 2012), 043619, 6 p.