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

## TL;DR

This paper investigates the spectral properties of a two-particle quantum system on the half-line with general interactions, establishing the essential spectrum, the existence of bound states below it, and finiteness of discrete eigenvalues.

## Contribution

It characterizes the essential spectrum and proves the existence and finiteness of bound states for a broad class of two-particle potentials on the half-line.

## Key findings

- Essential spectrum characterized
- Existence of eigenvalues below the essential spectrum proven
- Discrete spectrum contains finitely many eigenvalues

## 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.