# On a non-separable quantum many-particle system on the half-line

## TL;DR

This paper introduces and analyzes a one-dimensional quantum many-particle system on the half-line with unique interactions, providing a rigorous mathematical formulation and exploring its spectral properties.

## Contribution

It formulates a well-defined Hamiltonian for a non-separable two-particle system with novel interactions, advancing the mathematical understanding of such models.

## Key findings

- Defined the Hamiltonian as a self-adjoint operator
- Analyzed the spectral properties of the system
- Outlined future research directions

## Abstract

In this paper we will report on a one-dimensional, non-separable quantum many-particle system introduced in [arXiv:1504.08283,arXiv:1604.06693]. It consists of two (distinguishable) particles moving on the half-line being subjected to two different kinds of two-particle interactions: singular many-particle interactions localised at the origin and a binding-potential leading to a molecular-like state. We will formulate the model precisely, obtaining a well-defined self-adjoint operator (the Hamiltonian of our system) and elaborate on its spectral properties. In addition, we will present possible directions for future research.