量子力学的几何相
论文编号:WLX102 字数:13915,页数:31 摘 要 相位问题是量子力学中的重要问题，在20世纪曾经引起极大地争论。在经典的电动力学中，场强是表示电磁场性质的基本物理量，矢势只是数学上的表达，而在量子力学当中，场强是欠定的，势具有重要的物理意义。AB效应的发现出乎了很多人的意料，使人们对量子相位所隐藏着的物理规律给予足够的重视。量子力学相位理论的渗透发展，推动了量子信息科学的发展，它蕴含着深奥的物理思想。本文以势为基本点，讨论AB效应、AC效应、Berry相位、Aharonov―Anadan相位的形成及其实验验证过程，阐释量子几何相位与传统的相位观点的区别。以二态体系为主要例子，对Berry型相位的几何意义及其对体系过程当中的参数条件进行分析，在此基础上比较Berry相和Aharonov―Anadan相的区别与联系，讨论利用量子不变量求解Berry型相位的过程。关键词：AB效应 Berry相位 量子不变量 Aharonov―Anadan相 实验验证Abstract In quantum mechanics , phase problem is an important issue , and has aroused fierce controversy in the 20th century . In the classical electrodynamics , the field strength is a basic physical quantity which describe the nature of electromagnetic field , and the vector potential is just a mathematical expression , but in quantum mechanics , the field strength can not describe the field completely , and the vector potential has important physical meanings . The discovery of AB effect beyond many people's expectations , so that people pay more attention to the laws of physics that hidden behind the quantum phase . Quantum mechanics has been applied in many aspects of modern technologies and promotes the development of quantum information science , it contains profound physical thinkings . This article uses vector potential as the basic point to discuss the formation of these effects such as AB effect , AC effect , Berry’s phase and Aharonov-Anadan phase and describes the process of experimental verifications of these effects , explains the differences between geometric phase of quantum mechanics and the phase which considered in traditional views . This article uses the two state system as the main example , analysis the geometric significance of Berry’s phase and its conditions on the parameters in this system , on the basis of these , comparing the differences between Berry’s phase and Aharonov-Anadan phase and the links between them , discussing the process of using quantum invariant to solve Berry’s phase .Keywords: AB effect Berry's phase Aharonov-Anadan phase quantum invariant experimental verifications 目 录中文摘要..1英文摘要..2目录3第一章 引言..1第二章 A―B效应及其几何相问题..2 2.1 电磁场和相位因子2 2.2 Aharonov―Bohm效应及其实验验证4 2.3 Aharonov―Carmi效应8 2.4 Aharonov―Casher效应..10 第三章 Berry相及其物理意义..12 3.1 绝热近似和Berry相..12 3.2 Berry相与AB相的关系.15 3.3 Berry相的几何意义..17 3.4 Berry型相位的求解..19第四章 Berry相的实验验证.22第五章 结论与展望..25参考文献.26致谢..28
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