Bound states of a pair of particles on the half-line with a general interaction potential

Abstract

In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a main result, the existence of eigenvalues below the bottom of it. We also prove that the discrete spectrum contains only finitely many eigenvalues.

References in corpus (4)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• 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

Cited by in corpus (3)

• Boundary Superconductivity in the BCS Model
• Two-Particle Bound States at Interfaces and Corners
• On the number of isolated eigenvalues of a pair of particles in a quantum wire