力学量随时间的演化与对称性

文档编号:WLX065  字数:8942,页数:21

摘要
 量子力学中力学量随时间的演化的问题，与经典力学有所不同，经典力学中，处于一定状态下的体系的每一个力学量A，作为时间的函数在每一时刻都具有一个确定值。量子力学中，处于量子态下的体系，在每一时刻不是所有力学量都具有确定值，而只具有确定的几率分布和平均值。量子力学中, 守恒量与体系对称性之间有着密切联系。 此外，在用量子力学处理各种具体问题时，能严格求解者极少,而借助于对称体系的分析，就不必严格求解薛定谔方程，往往可以得出一些很重要的结论。本文主要分析了量子力学中力学量随时间的演化问题，介绍了薛定谔表象与海森伯表象，阐述了守恒量与对称性的关系，以及全同粒子系与波函数的交换对称性。
 
关键词：量子力学  随时间演化  守恒量  对称性  表象
 
 
Abstract
 In classical mechanics, a mechanical system volume over time in general is changing. But possibly has certain mechanical quantities, maintains invariable in the rate process, this kind of mechanical quantity is called the conservation quantity. In the quantum mechanics, between the conservation quantity and the system symmetry has the close relation. In addition, when uses the quantum mechanics deals with each kind of concrete issue, can the strict demander be extremely few, but with the aid in the symmetrical system's analysis, does not need to solve the Schrödinger equation strictly, often may draw some very important conclusion. In this article summary analysis quantum mechanic's conservation quantity and the symmetry, and have analyzed between symmetrical and the conservation quantity relations. And has involved, in quantum mechanics symmetry three deductions (conservation law, energy degeneracy, selection rule), Schrödinger equation symmetry and law of conservation of energy, mechanical quantity along with time evolution and symmetrical relations, all with granule system's symmetrical analysis. 
Keywords：Quantum mechanics；Evolution over time；Conserved quantity； Symmetry； representation.
 
目  录
中文摘要………………………………………………………………………………………ⅰ
英文摘要………………………………………………………………………………………ⅱ
目录……………………………………………………………………………………………ⅲ
第一章：绪论………………………………………………………………………………… 1
第二章：力学量随时间的演化……………………………………………………………… 2
  2.1 守恒量………………………………………………………………………………… 2
  2.2 能级简并与守恒量的关系…………………………………………………………… 3
第三章：薛定锷表象与海森伯表象………………………………………………………… 5
第四章：守恒量与对称性…………………………………………………………………… 8
  4.1 守恒量与对称性关系………………………………………………………………… 8
  4.2 宇称守恒……………………………………………………………………………… 10
第五章：全同粒子与波函数的交换对称分析……………………………………………… 12
结束语………………………………………………………………………………………… 16
致谢…………………………………………………………………………………………… 17
参考文献……………………………………………………………………………………… 18

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