一维量子体系的有限差分求解:(1)基本概念和无限深势阱  

Finite Difference Solution of One-Dimensional Quantum Systems:(1)Fundamental Concepts and Infinite Square Well

作　　者：任浩 赵文 戴昉纳 郭文跃 Hao Ren;Wen Zhao;Fangna Dai;Wenyue Guo(Shandong Key Laboratory of Intelligent Energy Materials,School of Materials Science and Engineering,China University of Petroleum(East China),Qingdao 266580,Shandong Province,China)

机构地区：[1]中国石油大学(华东),材料科学与工程学院,山东省智能能源材料重点实验室,山东青岛266580

出　　处：《大学化学》2025年第3期124-131,共8页University Chemistry

基　　金：国家自然科学基金(22473114);山东省自然科学基金(ZR2023MB034);中国石油大学(华东)研究生课程建设项目课程思政示范课(UPCYKS-2024-05)。

摘　　要：基于Python语言实现了教学代码,通过数值计算验证了正交归一性、本征能谱、不确定关系等量子力学基本概念,可用于化学、材料等专业结构化学相关课程的教学或数值实验。本文介绍的方法可扩展至更复杂的一维体系,如简谐或非谐振动、类氢原子径向波函数求解、双势阱、多势阱等常见的化学问题。近年来在我校材料化学专业的教学实践表明,多数同学可接受所授内容并独立实现计算代码,加深了对课程内容的理解。A Python-based teaching code has been developed to numerically verify fundamental quantum mechanical concepts,such as orthonormality,eigen spectrum,and uncertainty relations.This tool is applicable for teaching or conducting numerical experiments in structural chemistry courses for students majoring in Chemistry,Materials Science,and related fields.The techniques described can be extended to more complex one-dimensional systems,including harmonic and anharmonic oscillators,the radial wavefunctions of hydrogen-like atoms,and double or multiple potential wells,which are common problems in chemistry.Teaching practices in materials chemistry program at UPC have shown that most students can understand the material and independently implement computational codes,thereby deepening their comprehension of course content.

关 键 词：一维量子体系 数值计算 有限差分 

分 类 号：G64[文化科学—高等教育学] O6[文化科学—教育学]