An algorithm for keeping unitary evolution of a wave function in time-dependent potential field
Received date: 2023-04-07
Online published: 2024-05-25
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.
宋家莹 , 董光炯 . 一个保证波函数在含时的势场中幺正演化的算法[J]. 华东师范大学学报（自然科学版）, 2024 , 2024(3) : 121 -127 . DOI: 10.3969/j.issn.1000-5641.2024.03.013
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.
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