大学物理 ›› 2026, Vol. 45 ›› Issue (3): 80-.doi: 10.16854/j.cnki.1000-0712.250228

• 物理学史与物理学家 • 上一篇    下一篇

从概率幅到量子时代:玻恩规则的一百年

邢永忠,袁蓉,路飞平   

  1. 天水师范大学 物理系,甘肃 天水741000
  • 收稿日期:2025-04-30 修回日期:2025-06-18 出版日期:2026-05-15 发布日期:2026-06-04
  • 作者简介:邢永忠(1963 -),男,甘肃天水人,天水师范学院物理系教授,博士,主要从事物理学教学与原子核物理研究工作.
  • 基金资助:
    甘肃省一流本科课程《量子力学》建设项目(PX-16231111);国家自然科学基金项目(No.62465016;No.12465010)

From probability amplitudes to the quantum age: A century of the Born rule

XING Yongzhong,YUAN Rong,LU Feiping   

  1. Physics Department of Tianshui normal university, Tianshui 741000, Gansu, China
  • Received:2025-04-30 Revised:2025-06-18 Online:2026-05-15 Published:2026-06-04

摘要: 自1926年,马克斯·玻恩(Max Born)首次提出“波函数模平方即测量概率”以来,玻恩规则经历了整整一百年的理论检验与实验考验.本文以“从概率幅到量子时代”为主线,首先回顾该规则在旧量子论与新量子论交替时期的诞生背景,以及它如何彻底改变人们对物质微观行为的理解.随后,我们对玻恩规则在希尔伯特空间框架中的公理化表述做了简明解释,最后简要介绍了有关玻恩规则的研究新进展及其在现代科技中的应用.


关键词: 玻恩规则, 概率幅, 测量概率, 一百周年

Abstract: Since Max Born first stated in 1926 that the squared modulus of the wavefunction yields measurement probabilities, the Born rule has withstood a full century of theoretical scrutiny and experimental testing. Guided by the theme “from probability amplitudes to the quantum age,” this paper first reviews the historical setting in which the rule emerged during the transition from the old quantum theory to modern quantum mechanics and shows how it reshaped our understanding of microscopic phenomena. It then gives a concise explanation of the rule’s axiomatic formulation within the Hilbertspace framework. Finally, we outline recent advances in Bornrule research and survey its key applications in presentday quantum technology. 


Key words: Born rule, probability amplitude, measurement probability, centennial