A Python Program for Solving Schrödinger’s Equation in Undergraduate Physical Chemistry
A Python Program for Solving Schrödinger’s Equation in Undergraduate Physical Chemistry
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本科物理化学中求解薛定谔方程的 Python 程序
DOI：
10.1021/acs.jchemed.7b00003
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发表时间：
2017
影响因子：
3
通讯作者：
J. Madura
中科院分区：
文献类型：
--
作者：
Matthew N. Srnec;Shiv Upadhyay;J. Madura
在本科物理化学中，薛定谔方程在各种情况下都是求解的。在这样做时，系统的能量和波函数可以被解释为提供与正在研究的物理系统的联系。手动求解一维系统的这个方程是一项易于管理的任务，但是一旦学生打算进行各种更改并调查这些更改对结果的影响，就会变得非常耗时。为了解决这个问题，数值方法，如射击和线性有限差分方法，已被用来快速解决薛定谔方程。在本技术报告中，我们使用Python编程环境和三点有限差分数值方法来找到无限、有限、双有限、谐波、莫尔斯或Kronig-Penney有限势能阱中粒子的解并绘制结果（波函数或概率密度）。我们相信，这份技术报告将教育本科生的基本...
In undergraduate physical chemistry, Schrodinger’s equation is solved for a variety of cases. In doing so, the energies and wave functions of the system can be interpreted to provide connections with the physical system being studied. Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming once students aim to make various changes and investigate the impact of those changes on the results. To address this challenge, numerical methods, such as the shooting and linear finite-difference methods, have been utilized to quickly solve Schrodinger’s equation. In this technology report, we use the Python programming environment and the three-point finite-difference numerical method to find the solutions and plot the results (wave functions or probability densities) for a particle in an infinite, finite, double finite, harmonic, Morse, or Kronig–Penney finite potential energy well. We believe that this technology report will educate undergraduates on the basic ...