Rellich's theorem and N-body Schrodinger operators

TL;DR

This paper establishes an optimal version of Rellich's theorem for many-body Schrödinger operators, including models with singular potentials relevant to atoms and molecules, using Mourre estimates and localization techniques.

Contribution

It introduces an optimal Rellich theorem applicable to generalized many-body Schrödinger operators with singular potentials, advancing spectral analysis methods.

Findings

Proves an optimal Rellich theorem for many-body Schrödinger operators.

Extends applicability to models with singular potentials like atoms and molecules.

Utilizes Mourre estimates and functional calculus localization in the proof.

Abstract

We show an optimal version of the Rellich theorem for generalized many-body Schrodinger operators. It applies to singular potentials, in particular to a model for atoms and molecules with infinite mass and finite extent nuclei. Our proof relies on a Mourre estimate and a functional calculus localization technique.