目录 前言 第1章抽象群论1 1.0引言1 1.1抽象群的定义3 1.2抽象群的实例和群的乘法表4 1.3群元的重排定理9 1.4循环群9 1.5子群和陪集10 1.6有限群和置换群15 1.7共辄元素和类的结构19 1.8正规子群(不变子群)和商群22 1.9同构群和同态群25 本章小结26 习题27 第2章群表示理论28 2.1抽象群的矩阵表示29 2.2不可约表示的基本定理一一正交定理、舒尔引理34 2.3群表示的矩阵元正交定理38 2.4群表示的特征标44 2.5特征标表的构建49 2.6可约表示的分析51 本章小结60 习题61 第3章群表示理论在量子力学中的应用63 3.1坐标变换和群表示63 3.2薛定诗方程群75 3.3薛定诗方程群的表示78 3.4群论和好量子数80 3.5阿贝尔群的实际表示81 3.6不可约表示的基函数84 3.7直积群和直积表示94 3.8一个群自身的直积表示101 本章小结106 习题108 第4章晶体的32点群110 4.1晶体的对称性操作110 4.2晶体点群112 4.3点群的不可约表示122 4.4正则变换群127 4.5热力学方程群135 本章小结136 习题137 第5章群论在晶场中的应用139 5.1三维旋转群的基本性质139 5.2晶场141 5.3中间晶场劈裂情况147 5.4弱晶场情况和晶体双群159 5.5中间场情况的自旋效应166 5.6群论的矩阵元定理168 5.7选择定则和宇称176 5.8强场情况189 本章小结193 习题196 参考文献198 附录A对称性点群的特征标表199 附录B205 第1章习题答案205 第2章习题答案218 第3章习题答案222 第4章习题答案245 第5章习题答案268 Contents Foreword Chaper 1 Abstract Group Theory 1 1.0 lntroduction 1 1.1 Definitions of Abstract Group 3 1.2 Illustrative Examples and Multiplication Table of Abstract Group 4 1.3 Rearrangement Theorem9 1.4 Cyclic Group 9 1.5 Subgroups and Cosets 10 1.6 Finite order Groups and Permutation Groups 15 1.7 Conjugate Elements and Class Structure19 1.8 Normal Di visors and F actor Groups22 1.9 lsomorphic Groups and Homomorphic Groups 25 Summary of This Chapter 26 Problems27 Chaper 2 Theory of Group Representations 29 2.1 Matrix Representations of Abstract Group 29 2.2 Fundamental Theorem of lrreducible Representation一一-The Orthogonality Theorem, Schur's Lemma 34 2.3 Orthogonality Theorem of Matrix-elements 38 2.4 The Character of a Representation44 2.5 Construction of Character Tables 49 2.6 Decomposition of Reducible Representations 51 Summary of This Chapter60 Problems 61 Chaper 3 Application of Representation Theory in Quantum Mechanics 63 3.1 Transformation of coordinates and Group Representations 63 3.2 The Group of the Schrodinger Equation75 3.3 Representations of the Schrodinger Equation Group78 3.4 Group Theory and Good Quantum Numbers80 3.5 Illustrative Representations of Abelian Groups 81 3.6 Basis Functions for Irreducible Representations 84 3.7 Direct-product Groups and Direct-product Representations 94 3.8 Direct-product Representations within a Group 101 Summary of This Chapter106 Problems 108 Chaper4 The crystallographic 32 Point Group 110 4.1 Crystal-symmetry Operators110 4.2 The Crystal10graphic Point Group 112 4.3 lrreducible Representations of the Point Groups 122 4.4 Groups of Regular Transformations 127 4.5 The Group of the Thermodynamic Equation 135 Summary of This Chapter136 Problems 137 Chaper 5 Application of Group Theory in Crystal-field 139 5.1 Basic Properties of the Three-dimensional Rotation Group 139 5.2 Crystal-field一一一Crystal-field Splitting of Atomic Energy Levels141 5.3 Crystal-field-splitting in the Medium-field Case 147 5.4 Weak-crystal-field Case and Crystal Double Groups159 5.5 Spin Effects in the Medium-field Case 166 5.6 Group-theoretical Matrix-element Theorems 168 5.7 Selection Rules and Parity 176 5.8 Strong-crystal-field Case189 Summary of This Chapter193 Problems 196 Reference198 Appendices A Character Tables for point-symmetry Groups 199 Appendices B205 Answers to the Problems of Chapter 1 205 Answers to the Problems of Chapter 2 218 Answers to the Problems of Chapter 3 222 Answers to the Problems of Chapter 4 245 Answers to the Problems of Chapter 5 268