波传播算法在量子力学中的应用及其数值模拟  

APPLICATION OF BEAM PROPAGATION METHOD IN QUANTUM MECHANICS AND ITS NUMERICAL SIMULATION

作　　者：张灿 周卫康 陈天 ZHANG Can;ZHOU Weikang;CHEN Tian(College of Physics,Beijing Institute of Technology,Beijing 100081)

机构地区：[1]北京理工大学物理学院,北京100081

出　　处：《物理与工程》2022年第5期150-156,共7页Physics and Engineering

基　　金：国家自然科学基金(11974046);北京理工大学教改项目(经典光学波传播方法展示量子力学现象)。

摘　　要：波传播算法是研究电磁场传播的常用方法,量子波传播算法是在波传播算法的基础上进行改进用以计算量子力学中薛定谔方程演化的算法。文章主要介绍了量子波传播算法的大概思路,并以一维无限深势阱、一维方势垒、含时薛定谔方程为例给出了通用的分析过程,通过与薛定谔方程的严格解析解进行对比,并给出了微观粒子的概率波函数随时间的演化图像,验证了该算法的正确性有效性。量子波传播算法编程方面并不复杂,具有结构简单、实用性强等特点。Wave propagation algorithm is a common method to study electromagnetic field propagation.Quantum wave propagation algorithm is an improved algorithm based on wave propagation algorithm to calculate the evolution of schrodinger equation in quantum mechanics.This paper mainly introduces the general idea of quantum wave propagation algorithm,and presents the general analysis process by taking one-dimensional infinite deep potential well,one-dimensional square potential barrier and time-dependent Schrodinger equation as examples.By comparing with the strict analytical solution of Schrodinger equation,the evolution image of probability wave function of micro particles with time is given,which verifies the correctness and effectiveness of the algorithm.The programming of quantum wave algorithm is not complicated,and has the characteristics of simple structure and strong practicability.

关 键 词：波传播算法 一维无限深势阱 一维势垒 含时薛定谔方程 

分 类 号：O413.1[理学—理论物理]