On numerical solutions of the time-dependent Schrödinger equation

IF 0.8 4区教育学 Q3 EDUCATION, SCIENTIFIC DISCIPLINES

American Journal of Physics Pub Date : 2023-10-01 DOI:10.1119/5.0159866

Wytse van Dijk

引用次数: 1

Abstract

We review an explicit approach to obtaining numerical solutions of the Schrödinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with several examples. Because of its explicit nature, the algorithm can be readily extended to systems with a higher number of spatial dimensions. We show that the method also generalizes the staggered-time approach of Visscher and allows for the accurate calculation of the real and imaginary parts of the wave function separately.

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时间相关Schrödinger方程的数值解

我们回顾了一种明确的方法来获得Schrödinger方程的数值解，它在概念上是直截了当的，并且具有显著的准确性和效率。算例说明了该方法的有效性。由于其显式性质，该算法可以很容易地扩展到具有更高数量空间维度的系统。我们表明，该方法还推广了Visscher的交错时间方法，并允许分别精确计算波函数的实部和虚部。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Physics 物理-物理：综合

CiteScore

1.80

自引率

11.10%

发文量

146

审稿时长

3 months

期刊介绍： The mission of the American Journal of Physics (AJP) is to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our audience generally reads outside their specialties to broaden their understanding of physics and to expand and enhance their pedagogical toolkits at the undergraduate and graduate levels.