论文标题
信封理论是一种教学工具
The envelope theory as a pedagogical tool
论文作者
论文摘要
信封理论是一种可靠且易于实现的方法，可以解决时间独立的schrödinger方程（特征值和特征向量）。解决多体系统特别有用，因为计算成本与粒子数量无关。本文的目的是双重的。首先，我们想让知道可能太少的方法。其次，我们还想证明该方法可以用作教学工具，这要归功于它的简单性和可获得的可靠结果。为了实现这些目标，信封理论应用于一个简单的问题，在一个维度中，软库仑电位$ -K/\ sqrt {x^2+d^2} $，其特征是偏见距离$ d $。这种相互作用用于研究激子，电子孔结合对，其中两个电荷在两个不同的一维区域（量子线）中保持分离。除了它的身体兴趣外，该系统从未接受过信封理论的处理。
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.
