量子力学中的角动量守恒  

CONSERVATION OF ANGULAR MOMENTUM IN QUANTUM MECHANICS

作　　者：范乐乐 王锋 曾天海[1] FAN Lele;WANG Feng;ZENG Tianhai(School of Physics,Beijing Institute of Technology,Beijing 100081)

机构地区：[1]北京理工大学物理学院,北京100081

出　　处：《物理与工程》2024年第5期127-131,共5页Physics and Engineering

基　　金：国家自然科学基金(11875086);北京市自然科学基金(1242026)。

摘　　要：最近发表的两篇文章(Int.J.Theor.Phys.,2020,59:229;《物理与工程》,2024,第四期:5)先后给出了物理量严格守恒和统计守恒的提法和更确切的表述,与量子力学中守恒量的表述有所不同。本文讨论的系统的哈密顿量算符不含时间,因而与总角动量自身、分量及平方算符都是对易的,这些量就都是守恒量。在孤立复合系统中,总角动量分量中有一个满足严格守恒,而子系统的只能统计守恒,这两种守恒都可以用本征值和本征函数来表达。角动量自身一般没有本征值和本征函数,不能用这些概念表达其严格守恒;虽然有角动量平方的本征值和本征函数,但也不能表达严格守恒;只能表达它们统计守恒。The recent two papers have successively proposed the concepts and more precise expressions of strict conservation or statistical conservation of physical quantities,which are different from the expression of a conserved quantity in quantum mechanics.The Hamiltonian operator of the system discussed in this paper are independent of time,so it is commutative with the operators of an angular momentum itself,its component and its square,so that all these quantities are conserved quantities.In an isolated composite system,one of the angular momentum components of the total system are strictly conserved,while the angular momentum components of the subsystems can only be conserved statistically,both of which can be expressed in terms of eigenvalues and eigenfunctions.Generally,angular momentum itself does not have eigenvalues and eigenfunctions,so it cannot be expressed as strict conservation in terms of these concepts.Although there are eigenvalues and eigenfunctions for the square of angular momentum,they cannot express strict conservation either.And they can only be expressed as statistical conservation.

关 键 词：严格守恒 统计守恒 纠缠态 直积态 角动量自身 

分 类 号：O413.1[理学—理论物理]