Numerical solving of the vibrational time-independent Schrodinger equation in one and two dimensions using the variational method

Jernej Stare; Janez Mavri

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Numerical solving of the vibrational time-independent Schrodinger equation in one and two dimensions using the variational method

机译：一维和二维振动与时间无关的薛定inger方程的变分法数值求解

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A program package for variational solving of the time-independent Schrodinger equation (SE) in one and two dimensions is described. The first part of the the program package includes the fitting program (FIT) with which the ab initio or DFT calculated points are fitted to a computationally inexpensive functional form. Proper fitting of the potential energy surface is crucial for the quality of the results. The second part of the package consists of a program for variational solving of the SE (2DSCHRODINGER) using either a shifted Gaussian basis set or the rectangular basis set proposed by Balint-Kurti and coworkers [J. Chem. Phys. 91 (1989) 3571]. The third part of the program package consists of the calculation of the expectation values, IR and Raman spectra XPECT), and the visualization of results (PLOT). The program package is applied to study a quantum harmonic oscillator and an intramolecular, strong hydrogen bond in picolinic acid N-oxide. For the former system analytical solutions exist, while for the latter system a comparison with the experimental data is made. The advantages and disadvantages of the applied methods are discussed.

机译：描述了用于一维和二维变分求解与时间无关的薛定inger方程（SE）的程序包。程序包的第一部分包括拟合程序（FIT），通过它可以将头算或DFT计算点拟合为计算上不昂贵的功能形式。势能面的正确安装对于结果的质量至关重要。程序包的第二部分包括一个程序，用于使用移位高斯基集或Balint-Kurti和同事提出的矩形基集对SE（2DSCHRODINGER）进行变分求解[J.化学物理91（1989）3571]。程序包的第三部分包括期望值的计算，IR和拉曼光谱XPECT，以及结果的可视化（PLOT）。该程序包用于研究吡啶甲酸N-氧化物中的量子谐波振荡器和分子内强氢键。对于前一种系统，存在解析解，而对于后一种系统，则与实验数据进行了比较。讨论了所应用方法的优缺点。

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《Computer physics communications》 |2002年第3期|共19页
作者
Jernej Stare; Janez Mavri;
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正文语种 eng
中图分类计算机的应用;
关键词
variational method; Schrodinger equation; hydrogen bond; vibrational spectroscopy; rectangular basis set; gaussian basis set;

机译：变分法;薛定inger方程;氢键;振动光谱;矩形基集;高斯基集;

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1. Numerical solving of the vibrational time-independent Schrodinger equation in one and two dimensions using the variational method [J] . Jernej Stare, Janez Mavri Computer physics communications . 2002,第3期

机译：一维和二维振动与时间无关的薛定inger方程的变分法数值求解
2. Program package for numerical solving time-independent Schrodinger equation for vibrational problems: Inclusion of coordinate dependent reduced masses [J] . Gordana Pirc, Janez Mavri, Jernej Stare Vibrational Spectroscopy: An International Journal devoted to Applications of Infrared and Raman Spectroscopy . 2012,第Null期

机译：用于数值求解的振动问题的数值求解时间求解的程序包：包含坐标依赖性降低的肿块
3. Variational Sturmian approximation: A nonperturbative method of solving time-independent Schrodinger equation [J] . Mostafazadeh A. Journal of Mathematical Physics . 2001,第8期

机译：变Sturmian逼近：一种非扰动方法，用于求解与时间无关的薛定inger方程
4. A Numerical Model for Solving Two Dimensional Poisson-Schrodinger Equation in Depletion All Around Operation of the SOI Four Gate Transistor [C] . Shafat Jahangir, Q. D. M. Khosru IEEE International Conference of Electron Devices and Solid-State Circuits . 2009

机译：SOI四门晶体管围绕运行耗尽二维泊松 - Schrodinger方程的数值模型
5. Globally Accessible Finite Element Method based Web-Solver for the Vibrational Schrodinger Equation and its Application to HC 3O Carbon Chain Free Radical, ZNCL 2+ and Hydroxyacetaldehyde. [D] . Zajac, Peter. 2013

机译：基于全球可访问的有限元法的振动薛定Sch方程的Web解算器及其在HC 3O碳链自由基，ZNCL 2+和羟基乙醛中的应用。
6. New extended (G’/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation [O] . Harun-Or- Roshid, M Ali Akbar, Md Nur Alam, -1

机译：解决非线性发展方程的新的扩展（G’/ G）展开方法：（3 + 1）维势-YTSF方程
7. Variational Sturmian approximation: a nonperturbative method of solving time-independent Schrodinger equation [O] . Mostafazadeh, Ali 2017

机译：变分Sturmian逼近：一种非扰动方法，其求解时间独立的Schrodinger方程
8. Comparison of Numerical Analysis Methods for Solving One-Dimensional Elliptic Differential Equations [R] . Smith, R. A. 1979

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Numerical solving of the vibrational time-independent Schrodinger equation in one and two dimensions using the variational method

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