大学物理 ›› 2023, Vol. 42 ›› Issue (9): 20-.doi: 10.16854/j.cnki.1000-0712.220523

• 教学讨论 • 上一篇    下一篇

坐标算符在动量表象中表示式的一种引入方法

丰秀蓉,王锋   

  1. 北京理工大学 物理学院,北京100081
  • 收稿日期:2022-10-20 修回日期:2023-01-01 出版日期:2023-10-16 发布日期:2023-10-18
  • 通讯作者: 王锋,E-mail: wangfeng01@tsinghua.org.cn
  • 作者简介:丰秀蓉(1995—),女,山西朔州市人,北京理工大学物理学院2019级博士研究生.
  • 基金资助:
    国家自然科学基金(11774030, 51735001);北京市自然科学基金(2192049)资助

A method of introducing the expression of coordinate operator in momentum representation

 FENG Xiu-rong, WANG Feng   

  1. College of Physics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2022-10-20 Revised:2023-01-01 Online:2023-10-16 Published:2023-10-18

摘要: 在量子力学教材中,坐标算符在动量表象中的表示只是给出最终的结果,很少提及其详细的推导过程,这将使学生在学习量子力学过程中产生相应的疑惑.还有的是利用自由粒子是平面波的基本假设和狄拉克δ函数来推导坐标算符在动量表象中的表示,比较抽象和复杂,在教学中不利于学生的深入理解.本文另辟新径通过在泰勒展开的基础上引入了泰勒平移的概念,最后根据对易关系和泰勒平移来推导坐标算符在动量表象中的表示.该方法在教学过程中具有启发性,更有利于学生对这部分内容的理解.

关键词: 泰勒平移, 对易关系, 坐标算符, 动量表象

Abstract:  In the textbook of quantum mechanics, the expression of coordinate operator in momentum representation only gives the final result, and the detailed derivation process is seldom mentioned, which will cause students to have corresponding doubts in the process of learning quantum mechanics. What is more,the expression of coordinate operator in momentum representation is deduced by using the basic assumption that free particle is plane waves and Dirac δ function, which is abstract and complex, and is not conducive to students in-depth understanding in the teaching process. In this paper, we introduce the concept of Taylor's translation on the basis of Taylor's expansion. According to the commutation relation and Taylors translation, the expression of coordinate operators in the momentum representation is derived. This method is enlightening in the teaching process and more conducive to the students understanding of this part of the content.


Key words: Taylor′s translation, commutation relation, coordinate operator, momentum representation