Time-dependent Hartree approximation for a one-dimensional system of bosons with attractiveδ-function interactions

The time-dependent Hartree approximation is compared with an exact solution for the scattering between two $N$-particle bound states in the case of a 1-dimensional system of bosons with attractive $\delta$-function interactions. It is shown that to leading order in $N$, the approximation is exact, and arguments are presented relating this asymptotic agreement to the nonsaturation of the bound states.