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

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.

References in corpus (2)

• Long-lived resonances at mirrors
• Two interacting particles on the half-line

Cited by in corpus (7)

• On pairs of interacting electrons in a quantum wire
• On bound electron pairs in a quantum wire
• Bound states of a pair of particles on the half-line with a general interaction potential
• Many-particle quantum graphs: A review
• Two-Particle Bound States at Interfaces and Corners
• A remark on the effect of random singular two-particle interactions
• On the number of isolated eigenvalues of a pair of particles in a quantum wire