在最小长度的作用下，连续统中的束缚态是普适的
Bound states in the continuum are universal under the effect of minimal length
摘要：
连续体中的束缚态（BIC）通常被认为是不寻常的现象。在这项工作中，我们提供了一种方法来分析粒子的束缚态的空间结构存在的最小长度，它可以用来找到BIC。结果表明，在最小长度的影响下，BIC是一种普遍现象。几个典型的潜在的例子，即，给出了无限深势阱、线性势、谐振子、量子弹跳子和库仑势等，说明了BIC的普适性。提供了前三个例子的波函数和能量。得到了一个条件，以确定是否BIC可以很容易地发现系统。利用该条件，我们发现尽管BIC是普遍现象，但由于受最小长度效应扰动的束缚连续态太弱而无法观测到，所以在许多普通环境中，它们往往很难被发现。这一结果与目前对BIC的实验结果一致。此外，我们揭示了一个机制的BIC。该机制解释了为什么目前的研究表明，束缚离散态是典型的，而BIC总是在某些特定的环境下，当不考虑最小长度。
英文摘要：
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.
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