量子微观体系的对称性

论文编号:WLX075  字数:8978,页数:23

摘要
 在经典力学中, 一个体系的力学量, 一般说来是随时间而不断变化的, 但可能存在某些力学量在运动过程中保持不变, 这种力学量被称为守恒量。 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。本论文简要分析了量子力学中的守恒量和对称性，并分析了对称性与守恒量之间的关系。其中涉及了，量子力学对称性中的三个推论（守恒律，能量的简并性，选择定则），薛定谔方程的对称性与能量守恒定律，力学量随时间的演化与对称性的关系，全同粒子体系的对称性分析等。
 
 
关键词：量子力学 对称性 守恒量 微观体系 时空对称
 
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；Symmetry；Conservation quantity； Microscopic system； Space and time symmetry.
 
目  录
中文摘要…………………………………………………………………………………………ⅰ
英文摘要…………………………………………………………………………………………ⅱ
目录………………………………………………………………………………………………ⅲ
第一章：绪论……………………………………………………………………………………1
第二章：量子力学中的对称性分析……………………………………………………………2
第三章：对称性与守恒量的关系………………………………………………………………4
第四章：力学量随时间的演化与对称性………………………………………………………7
第五章：薛定谔方程时间对称性与能量守恒定律……………………………………………9
第六章：全同粒子体系的对称性………………………………………………………………14
结束语……………………………………………………………………………………………18
致谢………………………………………………………………………………………………19
参考文献…………………………………………………………………………………………20

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