Threshold Bound States

TL;DR

This paper presents a simple iterative method to analyze how the coupling constant affects the binding energy of threshold bound states, and explains why such states are absent in higher dimensions.

Contribution

It introduces an easy-to-apply iterative algorithm for eigenvalue problems that elucidates the relationship between coupling and binding energy, and clarifies the dimensional dependence of threshold bound states.

Findings

Derived relationships between coupling constant and binding energy.

Explained the absence of threshold bound states in higher dimensions.

Provided a straightforward iterative approach for eigenvalue problems.

Abstract

Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher dimensions can be easily understood.