量子力学的几何相

文档编号: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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