Journal of Systems Engineering and Electronics ›› 2010, Vol. 32 ›› Issue (10): 2121-2123.doi: 10.3969/j.issn.1001-506X.2010.10.22

• 传感器与信号处理 • 上一篇    下一篇

基于时域有限差分方法求解薛定谔方程

况晓静1,2，吴先良2，黄志祥1，陈明生2   

  1. 1. 安徽大学电子科学与技术学院， 安徽 合肥 230039; 
    2. 合肥师范学院物理与电子工程系， 安徽 合肥 230061
  • 出版日期:2010-10-10 发布日期:2010-01-03

Solution of time-dependent Shrodinger equation based on finite difference time domain method

KUANG Xiaojing1,2，WU Xianliang2，HUANG Zhixiang1，CHEN Mingsheng2   

  1. 1. School of Electronic Science and Technology, Anhui Univ., Hefei 230039, China;
    2. Dept. of Physics and Electronic Engineering, Hefei Teachers College, Hefei 230061, China
  • Online:2010-10-10 Published:2010-01-03

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摘要：

时域有限差分(finite difference time domain, FDTD)方法广泛应用于电磁场仿真领域，并与量子力学理论相结合来求解时域薛定谔方程，然而数值计算中的稳定性研究缺少理论方面的探讨。基于冯·诺依曼的稳定性分析方法得到了时域薛定谔方程的一维以及多维的稳定性条件，并且讨论了在不同势能情况下该稳定性条件的表现形式。数值结果充分证明了结论的正确性。

Abstract:

The finite difference time domain (FDTD) method is widely used in numerical simulation of electromagnetic fields, and it is combined with quantum mechanics to solve the time-dependent Schrodinger equation. Nevertheless, researches in stability numerical computation often lack theoretical support. This paper mainly deals with the stability condition starting from one-dimensional and multi-dimensional time-dependent Schrodinger equations based on von Neumann stability analysis. Especially, different cases of potential energy are investigated to obtain the expressions. Numerical results show the correctness of the conclusion.

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