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Basic principles and theory required for developing a practical and intuitive understanding of quantum mechanics are exarnined. Animations , conceptual problems and practical applications are presented at the end of each chapter to help readers better visualize and understand quantum phenomena As the book is especially designed for bilingual teaching and learning , the characteristics of differences between eastern and western thought and presentations are considered with attempts to bridge those differences. The target audience is undergraduate students majoring in physics and other areas for which a basic knowledge of quantum mechanics is expected.

Preface 前言

Part I The Wave Funclion and Schrodinger Equalion

第一部分 波函数及薛定谔方程

Chapter 1 The wave function and Schrodinger equation 波函数和薛定谔方程 1

1.1 The wave-particle duality and matter wave 波粒工象性与物质波 1

1.2 Wave function and its statistica1 interpretation 波函数及其统计解释 5

1.3 The principle of superpos山on 态叠加原理 8

1.4 The Schradinger equation 薛定谔方程 9

Biography 人物档案 11

Essay 短文：Schrodinger cat and EPR paradox 薛定谔猫和EPR佯谬 14

Associated application 相关应用：TEM and SEM 透射及扫描电子显微镜 16

Animation and simulation 演示与模拟 18

Discussion questions 讨论问题 21

Exercises 习题 22

Chapter 2 Time-independent Schrodinger eqnation and its application in one dimension 定态薛定谔方程及其在一维问题中的应用 23

2.1 Time-independent Schradinger equation and the stationary state 定态薛定谔方程和定态 23

2.2 The bound state and discrete spectra 束缚态与分立谱 27

2.3 Reflection and transmission tunneling effect 反射与透射，隧穿效应 44

Biography 人物档案 54

Associated application 相关应用：STM 扫描隧道显微镜 55

Anima tion and sim ula tion 演示与模拟 56

Discussion questions 讨论问题 60

Exercises 习题 60

Part II Physical Observables and Representations

第二部分 可观测物理量及表象理论

Chapter 3 Physical observables and representations 可观测量及其表示理论 64

3.1 Observables and operators 力学量与算符 64

3.2 Eigenvalues and eigenvectors of Hermitian operators 厄米算符的本征值与本征矢量 71

3.3 Representations and their transformations 表象理论与表象变换 80

3.4 The uncertainty principle 不确定原理 89

3.5 Dirac notation and the occupation number representation 狄拉克符号与占有数表象 94

Biography 人物档案 102

Essay 短文：Heisenberg and matrix mechanics 海森伯与矩阵力学 102

Anima tion and sim ula tion 演示与模拟 103

Discussion questions 讨论问题 108

Exercises 习题 108

Part III Applicalions of Ihe Schrodinger Equalion in 3D

第三部分 薛定谔方程在三维空间中的应用

Chapter 4 A particle in a central field 中心力场中的粒子 110

4.1 A particle in a central field 中心力场中的粒子 110

4.2 The radial equation for an electron in the Coulomb potential 库仑场中运动电子的径向方程 118

4.3 The hydrogen atom 氢原子 124

Biography 人物档案 129

Essay 短文：Niels Bohr and his theory for the hydrogen atom 波尔和他的氢原子理论 130

Associated appli四，non 相关应用：Cluantum computer 量子计算机 131

Discussion questions 讨论问题 133

Exercises 习题 134

Part IV Approximalion Melhods

第四部分 近似方法

Chapter 5 Perturhation theory 微扰理论 135

5.1 Time-independent perturbation theory 定态微扰理论 136

5.2 Time-dependent perturbation theory 含时微扰理论 148

5.3 The adiabatic theorem 绝热理论 171

Biography 人物档案 174

Essay 短文：Berry phase Berry 相位 175

Associated application 相关应用：Laser 激光 177

Animation and simulation 演示与模拟 178

Discussion questions 讨论问题 180

Exercises 习题 182

Part V Spin and Idenlical Parlicle Syslem

第五部分 自旋和全同多粒子体系

Chapter 6 Spin and Identical Particle System 自旋和全同粒子体系 185

6.1 The Stern-Gerlach experiment and its interpretation 斯特恩-格拉赫实验及其解释 185

6.2 The deion of spin 自旋的描述 189

6.3 The Schrodinger equation of charged particles in an external electromagnetic field 带电粒子在外电磁场中的薛定诗方程 194

6.4 Total angular momentum 总角动量 199

6.5 Fine structure of alkali atoms 碱金属原子的精细结构 205

6.6 The Zeeman effect 塞曼效应 208

6.7 Characteristics of identical particIes 全同粒子的特征 212

6.8 The wave function for a system of identical particles 全同粒子体系的波函数 214

6.9 Wave functions for two-electron system 两电子体系的波函数 218

6.10 The helium atom 氮原子 224

Biography 人物档案 228

Essay 短文：Quantum entanglement and Bell theorem 量子纠缠与Bell定理 232

Associated application 相关应用：Bose-Einstein condensation 玻色爱因斯坦凝聚 234

Anima tion and simulation 演示与模拟 237

Discussion questions 讨论问题 239

Exercises 习题 240

References 参考文献 242

Appendices 附录 244

Index 索引 263

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