Bound states in the continuum are universal under the effect of minimal length

TL;DR

This paper demonstrates that bound states in the continuum (BICs) are universal phenomena influenced by minimal length effects, providing a method to analyze their structure and conditions for their observability across various potentials.

Contribution

It introduces a new method to analyze BICs considering minimal length effects and establishes their universality across different potential systems.

Findings

BICs are universal under minimal length effects.

A condition to identify BICs in systems is derived.

BICs are difficult to observe in ordinary environments due to weak perturbations.

Abstract

Bound states in the continuum (BICs) are generally considered unusual phenomena. In this work, we provide a method to analyze the spatial structure of particle's bound states in the presence of a minimal length, which can be used to find BICs. It is shown that the BICs are universal phenomena under the effect of the minimal length. Several examples of typical potentials, i.e., infinite potential well, linear potential, harmonic oscillator, quantum bouncer and Coulomb potential, et al, are provided to show the BICs are universal. The wave functions and energy of the first three examples are provided. A condition is obtained to determine whether the BICs can be readily found in systems. Using the condition, we find that although the BICs are universal phenomena, they are often hardly found in many ordinary environments since the bound continuous states perturbed by the effect of the minimal length are too weak to observe. The results are consistent with the current experimental results on BICs. In addition, we reveal a mechanism of the BICs. The mechanism explains why current research shows the bound discrete states are typical, whereas BICs are always found in certain particular environments when the minimal length is not considered.