Hello...
We have 3 fermions (s=1/2) at the ground state of a harmonic oscillator moving over the x-axis with a the classic hamiltonian for a three particle oscillator :
H =(1/2m)*(P1)^2 +((1/2)*m(w^2)((x1)^2)) +(1/2m)*(P2)^2 +((1/2)*m(w^2)((x2)^2)) +(1/2m)*(P3)^2 +((1/2)*m(w^2)((x3)^2))
we...