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. Program summary Program Title:: 1d hydrogen light interactionProgram Files doi:: http://dx.doi.org/10.17632/2275fmvdzc.1Code Ocean Capsule:: https://doi.org/10.24433/CO.1476487.v1Licensing provisions:: MIT licenseProgramming language:: FORTRAN90Nature of problem:: 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 x = 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.Solution method:: 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.Additional comments including restrictions and unusual features:: 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.

中文翻译：

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一维时间相关薛定谔方程求解的数值方法比较

我们提出了一个简单的一维原子模型，该模型暴露于依赖于时间的强短脉冲 EM 场，目的是教本科生如何应用各种数值方法来研究该系统随时间演变的行为。几种时间传播方案。在这个模型中，精确的库仑势被软核相互作用代替，以避免原点的奇点。尽管该模型有一些缺点，但它已被证明是对全三维氢原子中发生的事情的合理表示。该模型可用作培养计算和软件开发领域的本科物理专业学生的工具。程序概要 Program Title:: 1d 氢光交互Program Files doi:: http://dx.doi.org/10.17632/2275fmvdzc.1Code Ocean Capsule:: https://doi.org/10.24433/CO。1476487.v1许可条款:: 麻省理工学院许可证编程语言:: FORTRAN90问题性质:: 一维时间相关薛定谔方程已被证明作为研究暴露于强短脉冲电磁场​​的氢原子的模型非常有用。我们使用在 x = 0 附近截止的模型势，避免了真实一维势的奇点，但保留了特征的里德堡级数和连续谱来研究真实 H 原子的激发和电离。该代码采用了多种数值方法来理解和比较应用于该模型问题时的有效性和准确性。解决方法:: 该程序使用并对比了多种方法；Crank-Nicolson、Short Iterative Lanczos、分裂算子的各种化身和 Chebychev 方法已经被编程。已使用空间坐标的 3 点有限差分 (FD) 离散化对这些方法进行了比较。为了完整起见，还对使用 5-9 FD 公式给予了一定的关注，以显示高阶离散化如何影响方法的准确性和效率，但该方法的主要重点是时间传播。其他评论包括限制和异常特征:: 该代码的主要目的是作为本科生的教学工具，有兴趣获得对实践计算物理学家有用的数值方法知识和编程技能。