量子力學(xué)的幾何相

應(yīng)用物理學(xué)論文編號:WLX102  字?jǐn)?shù):13915,頁數(shù):31

 目   錄
中文摘要..1
英文摘要..2
目錄3
第一章    引言..1
第二章   A—B效應(yīng)及其幾何相問題..2
 2.1     電磁場和相位因子2
 2.2    Aharonov—Bohm效應(yīng)及其實(shí)驗(yàn)驗(yàn)證4
 2.3    Aharonov—Carmi效應(yīng)8
 2.4    Aharonov—Casher效應(yīng)..10                                                                          
第三章   Berry相及其物理意義..12
 3.1    絕熱近似和Berry相..12
 3.2    Berry相與AB相的關(guān)系.15
 3.3    Berry相的幾何意義..17
 3.4    Berry型相位的求解..19
第四章   Berry相的實(shí)驗(yàn)驗(yàn)證.22
第五章   結(jié)論與展望..25
參考文獻(xiàn).26
致謝..28

 摘    要
 相位問題是量子力學(xué)中的重要問題，在20世紀(jì)曾經(jīng)引起極大地爭論。在經(jīng)典的電動力學(xué)中，場強(qiáng)是表示電磁場性質(zhì)的基本物理量，矢勢只是數(shù)學(xué)上的表達(dá)，而在量子力學(xué)當(dāng)中，場強(qiáng)是欠定的，勢具有重要的物理意義。AB效應(yīng)的發(fā)現(xiàn)出乎了很多人的意料，使人們對量子相位所隱藏著的物理規(guī)律給予足夠的重視。量子力學(xué)相位理論的滲透發(fā)展，推動了量子信息科學(xué)的發(fā)展，它蘊(yùn)含著深奧的物理思想。本文以勢為基本點(diǎn)，討論AB效應(yīng)、AC效應(yīng)、Berry相位、Aharonov—Anadan相位的形成及其實(shí)驗(yàn)驗(yàn)證過程，闡釋量子幾何相位與傳統(tǒng)的相位觀點(diǎn)的區(qū)別。以二態(tài)體系為主要例子，對Berry型相位的幾何意義及其對體系過程當(dāng)中的參數(shù)條件進(jìn)行分析，在此基礎(chǔ)上比較Berry相和Aharonov—Anadan相的區(qū)別與聯(lián)系，討論利用量子不變量求解Berry型相位的過程。
關(guān)鍵詞：AB效應(yīng)  Berry相位  量子不變量  Aharonov—Anadan相  實(shí)驗(yàn)驗(yàn)證

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