Two interacting particles on the half-line

Abstract

In the case of compact quantum graphs, many-particle models with singular two-particle interactions where introduced in [arXiv:1207.5648, arXiv:1112.4751] to provide a paradigm for further studies on many-particle quantum chaos. In this note, we discuss various aspects of such singular interactions in a two-particle system restricted to the half-line ${\mathbb{R}}_{+}$. Among others, we give a description of the spectrum of the two-particle Hamiltonian and obtain upper bounds on the number of eigenstates below the essential spectrum. We also specify conditions under which there is exactly one such eigenstate. As a final result, it is shown that the ground state is unique and decays exponentially as $\sqrt{x^2+y^2}\to \infty$.

17 pages

References in corpus (2)

• Two particles on a star graph I
• Two particles on a star graph II

Cited by in corpus (6)

• On a two-particle bound system on the half-line
• On pairs of interacting electrons in a quantum wire
• On bound electron pairs in a quantum wire
• Many-particle quantum graphs: A review
• Scattering properties of two singularly interacting particles on the half-line
• A remark on the effect of random singular two-particle interactions