Time-dependent Hartree approximation for a one-dimensional system of bosons with attractive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>δ</mml:mi></mml:math>-function interactions

Abstract

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 $\ensuremath{\delta}$-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.