华东师范大学学报（自然科学版） ›› 2024, Vol. 2024 ›› Issue (3): 121-127.doi: 10.3969/j.issn.1000-5641.2024.03.013

• 量子物理与量子信息处理 • 上一篇    

一个保证波函数在含时的势场中幺正演化的算法

宋家莹, 董光炯*()   

  1. 华东师范大学 精密光谱科学与技术国家重点实验室, 上海　200241
  • 收稿日期:2023-04-07 出版日期:2024-05-25 发布日期:2024-05-25
  • 通讯作者: 董光炯 E-mail:gjdong@phy.ecnu.edu.cn

An algorithm for keeping unitary evolution of a wave function in time-dependent potential field

Jiaying SONG, Guangjiong DONG*()   

  1. State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai　200241, China
  • Received:2023-04-07 Online:2024-05-25 Published:2024-05-25
  • Contact: Guangjiong DONG E-mail:gjdong@phy.ecnu.edu.cn

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摘要：

数值求解波函数的演化是量子力学研究的重要内容. 很多数值算法针对不含时的势能而发展; 然而有很多物理问题其势能是含时的, 在这种情况下, 以前发展的算法不能保证波函数幺正演化. 为此, 针对含时的势场发展了保证幺正演化的Crank-Nicolson算法, 同时采用四阶精度的Numerov算法实现了高精度的空间离散差分. 数值结果证明, 这个新算法能保证波函数演化的幺正性和稳定性.

关键词: 含时的势能, 含时Schr?dinger方程, Crank-Nicolson算法, Numerov算法

Abstract:

The numerical solution for wave function evolution plays an important role in quantum mechanics research. Many numerical algorithms have been developed for time-independent potential fields. However, multiple physical problems exist with the time-dependent potential. In this case, previously developed algorithms cannot guarantee the unitary evolution of wave function. In this study, the Crank-Nicolson algorithm to maintain unitary evolution in time-dependent potential fields is developed with a fourth-order accurate Numerov algorithm used to achieve high-precision spatial discretization. A numerical test demonstrates that the new algorithm maintains the unitarity and stability of wavefunction evolution.

Key words: time-dependent potential energy, time-dependent Schr?dinger equation, Crank-Nicolson algorithm, Numerov algorithm

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