维里定理及其对称性  

Virial theorem and its symmetry

作　　者：王怀玉[1] WANG Huaiyu(Department of Physics,Tsinghua University,Beijing,100084,China)

机构地区：[1]清华大学物理系,北京100084

出　　处：《华北科技学院学报》2021年第4期1-10,共10页Journal of North China Institute of Science and Technology

基　　金：国家重点研发计划资助项目(2018YFB0704304);国家自然科学基金(11074145,61275028);国家重大基础研究计划项目(2012CB927402,2016YFB0700102,2018YFB0704304)。

摘　　要：本文对于维里定理进行了详细全面的研究。对于量子力学维里定理的常用表达式给出了证明。对于经典力学和量子力学,都考虑了正动能物质和负动能物质的运动。每一种力学包括非相对论和相对论运动,都给出了维里定理的具体表达式。对于自旋1/2的单粒子和二粒子的情况做了仔细的讨论。对于各种相对论运动,都给出了低动量近似时的表达式。对于所有各种情况,都体现出维里定理关于正负动能的对称性。维里定理的这种对称性与物质运动的基本方程具有的对称性是一致的。一个正(负)动能粒子,只有受到吸引(排斥)作用,才能做稳定运动。In this work,Virial theorem is studied comprehensively.A proof is given for the Virial theorem in quantum mechanics.For classical mechanics and quantum mechanics,the motions of both positive kinetic energy(PKE)and negative kinetic energy(NKE)matters are considered.Each mechanics involves nonrelativistic and relativistic motions,and the concrete expressions of Virial theorem are presented.Detailed investigation is carried out for one and two spin 1/2 Dirac particles.In the cases of relativistic motions,the expressions for low momentum approximations are derived.For all the cases,Virial theorem shows symmetry with respect to PKE and NKE.This reflects the symmetry of the motion of the matter in our universe.A PKE(NKE)particle can do stationary motion only when it is subject to an attractive(repulsive)interaction.

关 键 词：经典力学的维里定理 量子力学的维里定理 低动量运动 相对论运动 二体系统 

分 类 号：O413.1[理学—理论物理]