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

## TL;DR

This paper investigates the approximation of the 1D Bose gas Hamiltonian with delta interactions by Schrödinger operators with rescaled potentials, providing convergence estimates in the norm resolvent sense.

## Contribution

It introduces a method to approximate the 1D Bose gas Hamiltonian with contact interactions using rescaled potentials and quantifies the convergence rate.

## Key findings

- Established norm resolvent convergence of the approximations
- Provided explicit estimates for the convergence rate
- Extended the understanding of contact interaction models in 1D Bose gases

## 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.