一个保证波函数在含时的势场中幺正演化的算法  

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

作　　者：宋家莹 董光炯 SONG Jiaying;DONG Guangjiong(State Key Laboratory of Precision Spectroscopy,East China Normal University,Shanghai200241,China)

机构地区：[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

出　　处：《华东师范大学学报（自然科学版）》2024年第3期121-127,共7页Journal of East China Normal University(Natural Science)

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.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.

关 键 词：含时的势能 含时Schr?dinger方程 Crank-Nicolson算法 Numerov算法 

分 类 号：O411.3[理学—理论物理]