一维粒子散射问题的计算机模拟及应用  

Computer simulation and simple application of one-dimensional particle scattering problems

作　　者：王哲 陈亮 WANG Zhe;CHEN Liang(School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《大学物理》2025年第3期42-47,共6页College Physics

基　　金：国家自然科学基金(12174101);中央高校基本科研业务费(2022MS051)。

摘　　要：一维量子散射问题是量子力学课程中的一个重要内容.在课程的教学过程中,人们往往只关注平面波的散射问题,对于更加真实的高斯波包的讨论比较少见.另一方面,人们往往只关注反射系数,透射系数等物理量的计算,对散射问题中的时间演化问题讨论较少.本工作中,我们使用Crank-Nicolson数值计算方法研究一系列高斯波包在一维势场中的含时演化问题.通过对有限高势垒散射、截断谐振子型势场散射、双势垒共振隧穿、Aharonov-Bohm效应等物理现象的研究,不仅可以加深我们对一维量子散射问题的理解,也为我们分析任意形状一维势中量子态的散射问题提供了一般方法.In(elementary)quantum mechanics,one-dimensional particle scattering is quite important.Due to the computational complexity of quantum mechanics,few models can clearly and intuitively qualitatively understand the whole process of one-dimensional particle scattering without manual solving,and even many models cannot obtain an analytical solution.Through computer simulation,it is not only possible to obtain the most accurate numerical solution in a very short time,but also to intuitively understand the process of one-dimensional scattering in the form of images and animations.In addition,through the simulation and analysis of several common examples,the understanding of one-dimensional scattering problems can be effectively deepened.

关 键 词：一维散射 计算机模拟 哈密顿矩阵 高斯波包 

分 类 号：O413[理学—理论物理]