Improvement of variational approach in an interacting two-fermion system

A more reasonable trial ground state wave function is constructed for the relative motion of an interacting two-fermion system in a one-dimensional (1D) harmonic potential. At the boundaries both the wave function and its first derivative are continuous and the quasi-momentum is determined by a more practical constraint condition which associates two variational parameters. The upper bound of the ground state energy is obtained by applying the variational principle to the expectation value of the Hamiltonian of relative motion on the trial wave function. The resulted energy and wave function show better agreement with the analytical solution than the original proposal.