包络理论作为一种教学工具
The envelope theory as a pedagogical tool
AI总结：
本文介绍包络理论这一计算成本与粒子数无关的本征问题求解方法，并以一维软库仑势中的激子系统为例，展示其作为可靠教学工具的价值。
摘要：
包络理论是求解不含时类薛定谔方程（特征值与特征向量）的一种可靠且易于实现的方法。它尤其适用于求解多体系统，因为其计算成本与粒子数无关。本文有两个目的。首先，我们希望介绍一种可能使用得太少的方法。其次，我们还希望表明，由于该方法的简单性以及能够获得的可靠结果，它可以作为一种教学工具。为实现这些目标，包络理论被应用于一个简单的一维问题，即以偏置距离 d 为特征的软库仑势 $-k/\sqrt{x^2+d^2}$。这种相互作用用于研究激子，即电子—空穴束缚对，其中两个电荷被保持分隔在两个不同的一维区域（量子线）中。除了其物理意义之外，该系统此前从未用包络理论处理过。
英文摘要：
The envelope theory is a reliable and easy to implement method to solve time independent Schrödinger-like equations (eigenvalues and eigenvectors). It is particularly useful to solve many-body systems since the computational cost is independent from the number of particles. The purpose of this paper is twofold. First, we want to make known a method that is probably too little used. Second, we also want to show that this method can be used as a pedagogical tool, thanks to its simplicity and the reliable results that can be obtained. To reach these goals, the envelope theory is applied to a simple problem in one dimension, the soft-Coulomb potential $-k/\sqrt{x^2+d^2}$, characterised by a bias distance $d$. Such interaction is used for the study of excitons, electron-hole bound pairs where the two charges are kept separated in two different one-dimensional regions (quantum wires). In addition to its physical interest, this system has never been treated with the envelope theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
