對(duì)稱(chēng)和凝聚態(tài)物理學(xué)中的計(jì)算方法

內(nèi)容概要

　　本書(shū)與其它傳統(tǒng)著作不同，巴塔努尼編著的《對(duì)稱(chēng)和凝聚態(tài)物理學(xué)中的計(jì)算方法》首次系統(tǒng)地介紹了現(xiàn)代物理學(xué)中三個(gè)非常重要的主題：對(duì)稱(chēng)、凝聚態(tài)物理和計(jì)算方法以及它們之間的有機(jī)聯(lián)系。本書(shū)展示了如何有效地利用群論來(lái)研究與對(duì)稱(chēng)性有關(guān)的實(shí)際物理問(wèn)題，首先介紹了對(duì)稱(chēng)性，進(jìn)而引入群論并詳細(xì)介紹了群的表示理論、特征標(biāo)的計(jì)算、直積群和空間群等，然后講解利用群論研究固體的電子性質(zhì)以及表面動(dòng)力學(xué)特性，此外還包括群論在傅立葉晶體學(xué)，準(zhǔn)晶和非公度系統(tǒng)中的高級(jí)應(yīng)用。本書(shū)包括大量的mathematica示例程序和150多道練習(xí)，可以幫助讀者進(jìn)一步理解概念。本書(shū)是凝聚態(tài)物理，材料科學(xué)和化學(xué)專(zhuān)業(yè)的研究生的理想教材。

書(shū)籍目錄

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 simple
characteristic
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 of
little-groups
appendix frobenius reciprocity theorem and other useful
theorems
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 onsager
relations
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 of
corepresentations
12.6 theory of crystal fields
12.7 onsager reciprocity theorem (onsager relations) and transport
properties
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-field
theories
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 ewald
summation
appendix 2 electronic effects on phonons in insulators and
semiconductors
exercises
16 experimental measurements and selection rules
16.1 introduction
16.2 selection rules
16.3 differential scattering cross-sections in the born
approximation
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 and
superlattices
18.3 quasi-crystal symmetry: the notion of indistinguishability and
the clossification of space-groups
18.4 two-dimensional lattices, cyclotomic integers, and axial
stacking
bibliography
references
index

章節(jié)摘錄

版權(quán)頁(yè)：   插圖：   The application of group theory to study physical problems and their solutions provides a formal method for exploiting the simplifications made possible by the presence of symmetry． Often the symmetry that is readily apparent is the symmetry of the system/object of interest， such as the three—fold axial symmetry of an NH3 molecule． The symmetry exploited in actual analysis is the symmetry of the Hamiltonian． When alluding to sym—metry we usually include geometrical， time—reversal symmetry， and symmetry associated with the exchange of identical particles． Con，servation laws of physics are rooted in the symmetries of the underlying space and time． The most common physical laws we are familiar with are actually marufestations of some universal symmetries． For example， the homogeneity and isotropy of space lead to the conservation of linear and angular momentum， respectively， while the homogeneity of time leads to the conservation of energy． Such laws have come to be known as universal conservation laws． As we will delineate in a later chapter， the relation between these classical symmetries and corresponding conserved quantities is beautifully cast in a theorem due to Emmy Noether． At the day—to—day working level of t．he physicist dealing with quantum mechanics， the application of symmetry restrictions leads to familiar results，such as selection rules and characteristic transformations of eigenfunctions when acted upon by symmetry operations that leave the Hamiltonian of the system invariant． In a similar manner， we expect that when a physical system/object is endowed with special symmetries， these symmetries forge conservation relations that ultimately determine its physical properties． rIYaditionally， the derivation of the physical states of a system has been performed without invoking the symmetry properties， however， the advantage of taking account of symmetry aspects is that it results in great simplification of the underlying analysis， and it provides powerful insight into the nature and the physics of the system． The mathematical framework that translates these symmetries into suitable mathematical relations is found in the theory of groups and group representations． This is the subject we will try to elucidate throughout the chapters of this book． We kn，ozu this to be true because sinx is an odd function； sin（－x）＝－sin（x）．In evaluating this integral， we have taken advantage of the asymmetry of its integrand． In order to cast this problem in the language of symmetry we introduce two mathematical operations：/， which we will identify later with the operation of inversion， and which， for now， changes the sign of the argument of a function， i．e．If（x）＝f（－x）； and E， which is an identity operation， Ef（x）＝f（x）． This allows us to write Figure 1．1 shows schematically the plane of integration， with q3 and 8 indicating the sign of the function sin x． We may introduce a more complicated integrand function f（x，y）， and carry the integration over the equilateral triangular area shown in Figure 1．2．

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