On a two-particle bound system on the half-line

TL;DR

This paper extends a two-particle interaction model on the half-line to include additional interactions, analyzes the Hamiltonian mathematically, and investigates how singular interactions influence molecular-like states.

Contribution

It introduces a generalized model with additional interactions and performs spectral analysis to understand their effect on molecular states.

Findings

Spectral properties of the extended Hamiltonian analyzed.

Impact of singular interactions on molecular states studied.

Mathematical formulation of the generalized two-particle system provided.

Abstract

In this paper we provide an extension of the model discussed in [arXiv:1504.08283] describing two singularly interacting particles on the half-line. In this model, the particles are interacting only whenever at least one particle is situated at the origin. Stimulated by [arXiv:1503.08814] we then provide a generalisation of this model in order to include additional interactions between the particles leading to a molecular-like state. We give a precise mathematical formulation of the Hamiltonian of the system and perform spectral analysis. In particular, we are interested in the effect of the singular two-particle interactions onto the molecule.