Gharibnejad H, Schneider B I, Leadingham M, Schmale H J
National Institute of Standards and Technology, Gaithersburg, MD 20899, United States.
West Virginia Wesleyan College, Buckhannon, WV 26201, United States.
Comput Phys Commun. 2020;252. doi: https://doi.org/10.1016/j.cpc.2019.05.019.
We present a simple, one-dimensional model of an atom exposed to a time-dependent intense, short-pulse EM field with the objective of teaching undergraduates how to apply various numerical methods to study the behavior of this system as it evolves in time using several time propagation schemes.In this model, the exact Coulomb potential is replaced by a soft-core interaction to avoid the singularity at the origin. While the model has some drawbacks, it has been shown to be a reasonable representation of what occurs in the fully three-dimensional hydrogen atom.The model can be used as a tool to train undergraduate physics majors in the art of computation and software development.
1d hydrogen light interaction http://dx.doi.org/10.17632/2275fmvdzc.1 https://doi.org/10.24433/CO.1476487.v1 MIT license FORTRAN90 The one dimensional time dependent Schrödinger equation has been shown to be quite useful as a model to study the Hydrogen atom exposed to an intense, short pulse, electromagnetic field. We use a model potential that is cut-off near = 0 and avoids the singularity of the true 1-D potential, but retains the characteristic Rydberg series and continuum to study excitation and ionization of the true H atom. The code employs a number of numerical methods to understand and compare the efficacy and accuracy when applied to this model problem. The program uses and contrasts a number of approaches; the Crank-Nicolson, Short Iterative Lanczos, various incarnations of the split-operator and the Chebychev method have been programmed. These methods have been compared using a 3-point finite difference (FD) discretization of the space coordinate. For completeness, some attention has also been given to using 5-9 FD formulas in order to show how higher order discretization affects the accuracy and efficiency of the methods but the primary focus of the method is the time propagation. The main purpose of this code is as a teaching tool for undergraduates interested in acquiring knowledge of numerical methods and programming skills useful to a practicing computational physicist.
我们提出了一个简单的一维原子模型，该原子暴露于随时间变化的强短脉冲电磁场中，目的是教导本科生如何应用各种数值方法，使用几种时间传播方案来研究该系统随时间演化的行为。在这个模型中，精确的库仑势被软核相互作用所取代，以避免原点处的奇点。虽然该模型有一些缺点，但已被证明是对全三维氢原子中所发生情况的合理描述。该模型可作为一种工具，用于训练本科物理专业学生的计算和软件开发技能。
一维氢光相互作用 http://dx.doi.org/10.17632/2275fmvdzc.1 https://doi.org/10.24433/CO.1476487.v1 MIT许可 FORTRAN90 一维含时薛定谔方程已被证明是一个非常有用的模型，用于研究暴露于强短脉冲电磁场中的氢原子。我们使用一种在r = 0附近截断的模型势，它避免了真实一维势的奇点，但保留了特征里德伯系列和连续谱，以研究真实氢原子的激发和电离。该代码采用了多种数值方法，以理解和比较应用于这个模型问题时的有效性和准确性。该程序使用并对比了多种方法；已对克兰克 - 尼科尔森法、短迭代兰索斯法、分裂算符的各种变体以及切比雪夫法进行了编程。这些方法已使用空间坐标的三点有限差分（FD）离散化进行了比较。为了完整起见，还对使用5 - 9点FD公式给予了一些关注，以展示高阶离散化如何影响这些方法的准确性和效率，但该方法的主要重点是时间传播。此代码的主要目的是作为一个教学工具，供对获取数值方法知识和对实践计算物理学家有用的编程技能感兴趣的本科生使用。
