大学物理 ›› 2024, Vol. 43 ›› Issue (5): 22-.doi: 10.16854/j.cnki.1000-0712.230226

• 教学讨论 • 上一篇    下一篇

德布罗意物质波关系式的推导

汪洋   

  1. 1. 中国科学技术大学 技术与创新支持中心,安徽 合肥230026;
    2. 中国科学院合肥物质科学研究院,安徽 合肥230031
  • 收稿日期:2023-06-11 修回日期:2023-08-19 出版日期:2024-06-20 发布日期:2024-07-04
  • 作者简介:汪洋(1987—),男,湖北蕲春人,中国科学技术大学技术与创新支持中心工程师,主要从事量子通信专利检索分析研究工作. E-mail: wy299792@ustc.edu.cn

Derivation ofthe De Broglie matter wave equation

WANG Yang   

  1. Technology and Innovation Support Center, University of Science and Technology of China, Hefei, Anhui 230026, China
  • Received:2023-06-11 Revised:2023-08-19 Online:2024-06-20 Published:2024-07-04

摘要: 本文通过2种直观的方式推导出物质波动量-波长关系式. 第1种方式利用洛伦兹变换得出运动粒子“首尾”两端固有时间差,进而通过其对应的相位差以及粒子在空间占据的长度得出相应的物质波波长;第2种方式通过计算与粒子相位变化相适配的行波,得出物质波动量-波长关系式.这两种推导方式较为直观,有助于初学者理解物质波的物理图像.

关键词: 物质波关系式, 洛伦兹变换, 相对论效应

Abstract: The equation for the momentum and the wavelength for the matter wave is derived in two intuitive ways. The first way is to use the Lorentz transformation to obtain the inherent time difference between the head and tail of the moving particles, and then obtain the corresponding wavelength for the material wave through its phase difference and the length of the particle occupied in space. The second way is to obtain the equation by calculating the traveling wave adapted to the phase change of the particle. These two derivation methods are intuitive and helpful to beginners to understand the physical image of the matter wave.

Key words: matter wave equation, Lorentz transformation, relativistic effect