Multiparticle Schrodinger operators with point interactions in the plane

TL;DR

This paper investigates the mathematical properties of a quantum system of multiple bosons in a plane with point interactions, establishing self-adjointness and energy bounds after renormalization.

Contribution

It demonstrates the self-adjointness of the Hamiltonian for multiparticle bosonic systems with point interactions in the plane, including regular potentials, and provides energy bounds.

Findings

Hamiltonian is self-adjoint after renormalization

Energy bounds are established for the system

Results extend to regular inter-particle potentials

Abstract

We study a system of N bosons in the plane interacting with delta function potentials. After a coupling constant renormalization we show that the Hamiltonian defines a self-adjoint operator and obtain a lower bound for the energy. The same results hold if one includes a regular inter-particle potential.