论文标题
以高精度求解一维时间独立的Schrödinger方程：Lagrangemesh Mathematica软件包
Solving the One-Dimensional Time-Independent Schrödinger Equation with High Accuracy: The LagrangeMesh Mathematica Package
论文作者
论文摘要
为了找到与一维schröodinger方程相关的频谱，我们讨论了Lagrange网格方法（LMM）及其对绑定状态的数值实现。在介绍了LMM背后的理论的一般概述之后，我们介绍了Lagrangemesh软件包：Mathematica中LMM的数值实现。该软件包使用几行代码，可以对频谱进行快速的家庭计算机计算，并提供了研究量子力学中大量系统的实用工具。软件包的主要属性是（i）输入基本上是定义的潜在函数和间隔； （ii）用户可以控制计算和最终结果的准确性。作为说明，通过采用软件包提供的命令，可以获得一些相关量子系统的高度准确的频谱。实际上，根据工作示例，目前的工作可以视为用户指南。
In order to find the spectrum associated with the one-dimensional Schröodinger equation, we discuss the Lagrange Mesh method (LMM) and its numerical implementation for bound states. After presenting a general overview of the theory behind the LMM, we introduce the LagrangeMesh package: the numerical implementation of the LMM in Mathematica. Using few lines of code, the package enables a quick home-computer computation of the spectrum and provides a practical tool to study a large class of systems in quantum mechanics. The main properties of the package are (i) the input is basically the potential function and the interval on which is defined; and (ii) the accuracy in calculations and final results is controllable by the user. As illustration, a highly accurate spectrum of some relevant quantum systems is obtained by employing the commands that the package offers. In fact, the present work can be regarded as a user guide based on worked examples.
