大学物理 ›› 2025, Vol. 44 ›› Issue (8): 1-.doi: 10.16854/j.cnki.1000-0712.250210

• 专家视点 •    下一篇

量子力学:哥廷恩出品

曹则贤   

  1. 中国科学院物理研究所,北京100190
  • 收稿日期:2025-04-17 修回日期:2025-04-26 出版日期:2025-11-03 发布日期:2025-11-03
  • 作者简介:曹则贤(1966—),男,中国科学院物理所研究员,博导,主要从事表面物理、量子力学等方面的研究

Quantenmechanik:Produkt aus G-ttingen

CAO Zexian   

  1. Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2025-04-17 Revised:2025-04-26 Online:2025-11-03 Published:2025-11-03

摘要: 虽然产自瑞士的薛定谔波力学和产自英国的狄拉克相对论量子力学是一般文献中的量子力学主体,依然不妨说量子力学是哥廷恩的产品,从思想、概念与数学方法上它都是源自哥廷恩.哥廷恩大学毕业的黎曼首次于1854年将Quanta的概念引入几何,1893-1900年间哥廷恩大学毕业的维恩利用Energiequantum (能量量子), Arbeisquantum(功量子), Wrmequantum(热量子)的概念研究黑体辐射.携一众弟子构造了原子物理/量子论的索末菲是在哥廷恩的克莱因门下做的Habilitation,其1919年的bermechanik (超力学)可以说是量子力学概念的前身.1924年,哥廷恩大学希尔伯特和库朗合著的《数学物理方法》面世,同年玻恩提出了“Quantenmechanik (量子力学)”一词,约当在玻恩门下获得物理学博士学位.1925年,在哥廷恩作为玻恩助手的海森堡将克拉默斯色散关系改造成了量子论的形式,玻恩-约当构造了矩阵力学.玻恩懂矩阵代数是因为此前闵可夫斯基专门派人辅导他矩阵知识以备研究相对论用的.约当还是提出量子场论和量子生物学的第一人. 1926年玻恩提出了薛定谔波函数的概率诠释.1927年在哥廷恩进修数学的冯瘙簚诺依曼开启了量子力学公理化,特别是提出了希尔伯特空间的概念.哥廷恩大学毕业的外尔解了氢原子问题的薛定谔方程,并将群论应用于量子力学研究,另一位将群论应用于量子力学的维格纳那段时间在哥廷恩做希尔伯特的助手. 其他的对量子力学建立有贡献的如泡利 (索末菲的学生,曾做过玻恩的助手)等也都和哥廷恩有渊源.一句话,量子力学这样的一门哲学意义深厚的数学物理只能是哥廷恩出品.

关键词: 量子力学, 量子论, 数学物理, 哥廷恩

Abstract: Although the wave mechanics was developed by Austrian Schrdinger in Swiss and the relativistic quantum equation was derived by British Dirac, yet we can safely say that quantum mechanics is a product of Gttingen, a conclusion easy to arrive when the relevant ideas, concepts and methodology are evaluated in an objective manner. It is Riemann who first introduced in 1854 the concept of Quanta into geometry, and in publications of Wien in the period of 1893-1900 the concepts such as Energiequantum (energy quantum), Arbeisquantum (work quantum), Wrmequantum( heat quantum) were to be seen frequently. Sommerfeld, one who created the atomic physics with his many gifted disciples, completed his Habilitation under Klein, and the concept of bermechanik (Supermechanics) proposed by him in 1919 can be understood as the precursor of quantum mechanics. Born lectured in 1923/1924 over Atommechnik (atom mechanics), and coined the word Quantenmechanik (quantum mechanics) in a paper in 1924. At the same year, the book Methoden der mathematischen Physik coauthored by Hilbert and Courant was published, and in the preface Courants assistant Jordan was acknowledged. In 1925, inspired by Heisenbergs quantum theoretical formulation of the Kramers dispersion relation, Born and Jordan, the latter just got his Ph.D. degree under Born, constructed the matrix mechanics. Born was familiar with matrix algebra since in 1908 Minkowski had let Toeplitz to teach him that subject to prepare for his research over relativity. Jordan later initiated the research over quantum field theory and quantum biology. In 1926, Born put forward the probability interpretation to Schrdingers wavefunction. In 1927, Heisenberg published his seminal paper over the uncertainty principle, von Neumann began his effort to axiomatize quantum mechanics, Weyl taught and researched on group theory and quantum mechanics in Zurich, and Wigner also began to explore the application of group theory in quantum mechanics. All these heroes of quantum mechanics are graduate student and/or staff member of University Gttingen, and they all benefited from the mathematical tradition of Gttingen that had been established by Gauss, Riemann, Klein, Hilbert, Minkowski, etc. The basic concepts in quantum mechanics such as eigenvalue problem, eigenvalue spectrum of operators, vector space and so on are all originated in Gttingen. In a word, quantum mechanics, a branch of mathematical physics full of philosophical color, is, and it can only be, the product of Gttingen.

Key words: quantum mechanics, quantum theory, mathematical physics, Gttingen