For a system of N bosons in one space dimension with two-body δ-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 Schrödinger operators with rescaled two-body potentials, and we estimate the rate of this convergence. Keywords Many-body quantum system • Short-range interaction • Contact interaction • Bose gas • Schrodinger operator with singular interactions • Konno-Kuroda formula • Gamma convergence

Quantum systems composed of N distinct particles in $$\mathbb {R}^2$$ R 2 with two-body contact interactions of TMS type are shown to arise as limits—in the norm resolvent sense—of Schrödinger operators with suitably rescaled pair potentials.

Ultracold quantum gases of equal spin fermions with short range interactions are often considered free even in the presence of strongly binding spin-up-spin-down pairs. We describe a large class of many-particle Schrödinger operators with short-range pair interactions, where this approximation can be justified rigorously.

Ultracold quantum gases of equal-spin fermions with short-range interactions are often considered free even in the presence of strongly binding spin-up–spin-down pairs. We describe a large class of many-particle Schrödinger operators with short-range pair interactions, where this approximation can be justified rigorously.