From Short-Range to Contact Interactions in the 1d Bose Gas

Abstract

For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schr\"odinger operators with rescaled two-body potentials, and we estimate the rate of this convergence.