求解Schrödinger方程的一种新能量守恒格式  

A New Energy Conservation Scheme for Solving Schrödinger Equations

作　　者：王雅慧 WANG Ya-hui(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,浙江杭州310018

出　　处：《兰州文理学院学报(自然科学版)》2025年第2期29-33,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：针对一维非线性Schrödinger方程,通过使用多标量辅助变量方法将原方程转化为具有能量守恒性质的等价系统.对等价系统构建带有惩罚项的数值格式,该格式保持修正的能量守恒,并且在每一个时间步长只需求解带有常系数矩阵的解耦系统.最后通过数值实验验证了该数值格式的有效性.For the one-dimensional nonlinear Schrödinger equations,the multiple scalar auxiliary variable method is used to transform the original equation into an equivalent system with energy conservation property.A numerical scheme with penalty term is constructed for solving the equivalent system.The scheme preserves the modified energy conservation,and only needs to solve the decoupling system with constant coefficient matrix at each time step.Finally,the validity of the numerical scheme is verified by numerical experiments.

关 键 词：Schr?dinger方程 多标量辅助变量 能量守恒 

分 类 号：O241.82[理学—计算数学]