对称和凝聚态物理中的计算方法（英文版 影印本）
出版时间：2012年版
内容简介
本书与其它传统著作不同，巴塔努尼编著的《对称和凝聚态物理学中的计算方法》首次系统地介绍了现代物理学中三个非常重要的主题：对称、凝聚态物理和计算方法以及它们之间的有机联系。本书展示了如何有效地利用群论来研究与对称性有关的实际物理问题，首先介绍了对称性，进而引入群论并详细介绍了群的表示理论、特征标的计算、直积群和空间群等，然后讲解利用群论研究固体的电子性质以及表面动力学特性，此外还包括群论在傅立叶晶体学，准晶和非公度系统中的高级应用。本书包括大量的mathematica示例程序和150多道练习，可以帮助读者进一步理解概念。本书是凝聚态物理，材料科学和化学专业的研究生的理想教材。
目 录
preface
1 symmetry and physics
1.1 introduction
1.2 hamiltonians, eigenfunctions, and eigenvalues
1.3 symmetry operators and operator algebra
1.4 point-symmetry operations
1.5 applications to quantum mechanics
exercises
2 symmetry and group theory
2.1 groups and their realizations
2.2 the symmetric group
2.3 computational aspects
2.4 classes
2.5 homomorphism, isomorphism, and automorphism
2.6 direct- or outer-product groups
exercises
3 group representations: concepts
3.1 representations and realizations
3.2 generation of representations on a set of basis functions
exercises
4 group representations: formalism and methodology
4.1 matrix representations
4.2 character of a matrix representation
4.3 burnside's method
exercises
computational projects
5 dixon's method for computing group characters
5.1 the eigenvalue equation modulo p
5.2 dixon's method for irreducible characters
5.3 computer codes for dixon's method
appendix 1 finding eigenvalues and eigenvectors
exercises
appendix 2
computation project
6 group action and symmetry projection operators
6.1 group action
6.2 symmetry projection operators
6.3 the regular projection matrices: the simplecharacteristic
exercises
7 construction of the irreducible representations
7.1 eigenvectors of the regular rep
7.2 the symmetry structure of the regular rep eigenvectors
7.3 symmetry projection on regular rep eigenvectors
7.4 computer construction of irreps with ds ]1
7.5 summary of the method
exercise
8 product groups and product representations
8.1 introduction
8.2 subgroups and cosets
8.3 direct outer-product groups
8.4 semidirect product groups
8.5 direct inner-product groups and their representations
8.6 product representations and the clebsch-gordan series
8.7 computer codes
8.8 summary
exercises
9 induced representations
9.1 introduction
9.2 subduced reps and compatibility relations
9.3 induction of group reps from the irreps of its subgroups
9.4 irreps induced from invariant subgroups
9.5 examples of irrep induction using the method oflittle-groups
appendix frobenius reciprocity theorem and other usefultheorems
exercises
10 crystallographic symmetry and space-groups
10.1 euclidean space
10.2 crystallography
10.3 the perfect crystal
10.4 space-group operations: the seitz operators
10.5 symmorphic and nonsymmorphic space-groups
10.6 site-symmetries and the .wyckoff notation
10.7 fourier space crystallography
exercises
11 space-groups: irreps
11.1 irreps of the translation group
11.2 induction of irreps of space-groups
exercises
12 time-reversal symmetry: color groups and the onsagerrelations
12.1 introduction
12.2 the time-reversal operator in quantum mechanics
12.3 spin-l/2 and double-groups
12.4 magnetic and color groups
12.5 the time-reversed representation: theory ofcorepresentations
12.6 theory of crystal fields
12.7 onsager reciprocity theorem (onsager relations) and transportproperties
exercises
13 tensors and tensor fields
13.1 tensors and their space-time symmetries
13.2 construction of symmetry-adapted tensors
13.3 description and classification of matter tensors
13.4 tensor field representations
exercises
14 electronic properties of solids
14.1 introduction
14.2 the one-electron approximations and self-consistent-fieldtheories
14.3 methods and techniques for band structure calculations
14.4 electronic structure of magnetically ordered systems
appendix i derivation of the hartree-fock equations
appendix 2 holstein-primakoff (hp) operators
exercises
15 dynamical properties of molecules, solids, and surfaces
15.1 introduction
15.2 dynamical properties of molecules
15.3 dynamical properties of solids
15.4 dynamical properties of surfaces
appendix 1 coulomb interactions and the method of ewaldsummation
appendix 2 electronic effects on phonons in insulators andsemiconductors
exercises
16 experimental measurements and selection rules
16.1 introduction
16.2 selection rules
16.3 differential scattering cross-sections in the bornapproximation
16.4 light scattering spectroscopies
16.5 photoemission and dipole selection rules
16.6 neutron and atom scattering spectroscopies
exercises
17.1 phase transitions and their classification
17.2 landau theory of phase transitions: principles
17.3 construction and minimization techniques for △φ
exercises
18 incommensurate systems and quasi-crystals
18.1 introduction
18.2 the concept of higher-dimensional spaces: superspaces andsuperlattices
18.3 quasi-crystal symmetry: the notion of indistinguishability andthe clossification of space-groups
18.4 two-dimensional lattices, cyclotomic integers, and axialstacking
bibliography
references
index
