大学化学 >> 2025, Vol. 40 >> Issue (3): 408-414.doi: 10.12461/PKU.DXHX202407066

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从经典力学出发理解微观粒子的波粒二象性和量子化

杨翠翠1,2, 商波2, 陈效华2, 田维全2   

  1. 1 重庆理工大学理学院, 重庆 400054;
    2 重庆大学化学化工学院, 重庆 401331
  • 收稿日期:2024-07-22 录用日期:2024-10-10 发布日期:2025-03-19
  • 通讯作者: 田维全 E-mail:tianwq@cqu.edu.cn
  • 基金资助:
    重庆理工大学科研启动基金(2023ZDR022)；国家自然基金(21673025)；超分子结构与材料国家重点实验室开放项目(SKLSSM2023022);重庆大学化学工程与技术学科水平提升计划；重庆大学研究生重点课程资助(20210628)

Understanding the Wave-Particle Duality and Quantization of Confined Particles Starting from Classic Mechanics

Cuicui Yang1,2, Bo Shang2, Xiaohua Chen2, Weiquan Tian2   

  1. 1 College of Science, Chongqing University of Technology, Chongqing 400054, China;
    2 College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China
  • Received:2024-07-22 Accepted:2024-10-10 Published:2025-03-19
  • Contact: Weiquan Tian E-mail:tianwq@cqu.edu.cn

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摘要： 有质量微观粒子的“波粒二象性”和“量子化”等是初学量子化学过程中必须理解但又难以理解的基本概念。本文以电子的能量方程和动量算符出发讨论微观粒子的波粒二象性、运动空间的限域化和能量的量子化，推理得出限域导致量子化的结论。

关键词: 微观粒子, 能量方程, 波粒二象性, 动量算符, 势场作用, 运动量子化

Abstract: “Wave-particle duality” and “quantization” of microscopic particles with mass are fundamental concepts but challenging for beginners learning quantum chemistry. The wave-particle duality, space-confinement of motion and quantization of energy of microscopic particles are discussed based on the energy equation and momentum operator in the present work. A conclusion that confinement leads to quantization of microscopic particles is reached.

Key words: Microscopic particles, Energy equation, Wave-particle duality, Momentum operator, Potential field interaction, Quantization of motion