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Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups [Mīkstie vāki]

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(Jesus College, Oxford University), (Carnegie Laboratory of Physics, University of Dundee, UK)
  • Formāts: Paperback / softback, 768 pages, height x width x depth: 244x189x36 mm, weight: 1227 g, 56 b/w line illustrations
  • Sērija : Oxford Classic Texts in the Physical Sciences
  • Izdošanas datums: 10-Dec-2009
  • Izdevniecība: Oxford University Press
  • ISBN-10: 0199582580
  • ISBN-13: 9780199582587
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Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space GroupsPalielināt
  • Formāts: Paperback / softback, 768 pages, height x width x depth: 244x189x36 mm, weight: 1227 g, 56 b/w line illustrations
  • Sērija : Oxford Classic Texts in the Physical Sciences
  • Izdošanas datums: 10-Dec-2009
  • Izdevniecība: Oxford University Press
  • ISBN-10: 0199582580
  • ISBN-13: 9780199582587
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780199582587.html
Keywords:
This book gives the complete theory of the irreducible representations of the crystallographic point groups and space groups. This is important in the quantum-mechanical study of a particle or quasi-particle in a molecule or crystalline solid because the eigenvalues and eigenfunctions of a system belong to the irreducible representations of the group of symmetry operations of that system. The theory is applied to give complete tables of these representations for all the 32 point groups and 230 space groups, including the double-valued representations. For the space groups, the group of the symmetry operations of the k vector and its irreducible representations are given for all the special points of symmetry, lines of symmetry and planes of symmetry in the Brillouin zone. Applications occur in the electronic band structure, phonon dispersion relations and selection rules for particle-quasiparticle interactions in solids. The theory is extended to the corepresentations of the Shubnikov (black and white) point groups and space groups.

Recenzijas

This book is written for the student of theoretical physics who wants to work in the eld of solids and for the experimenter with a knowledge of quantum theory who is not content to take other people's arguments for granted. * Zentralblatt Math *

Symmetry and the Solid State
1(50)
Introduction
1(6)
Group theory
7(8)
Group representations
15(9)
Point groups
24(13)
Space groups
37(14)
Symmetry-Adapted Functions for the Point Groups
51(30)
The matrix elements of the rotation group
51(3)
The generation of symmetry-adapted functions
54(2)
Application to the point groups
56(1)
Symmetry-adapted functions for the crystallographic point groups
57(19)
Active and passive operators
76(1)
Symmetrized and anti-symmetrized products of point-group representations
77(4)
Space Groups
81(90)
Bravais lattices
81(5)
Reciprocal lattices and Brillouin zones
86(9)
The classification of points and lines of symmetry
95(24)
The irreducible representations of the translation groups
119(2)
The classification of the 230 3-dimensional space groups
121(23)
The action of space-group operations on Bloch functions
144(2)
A descriptive account of the representation theory of space groups
146(15)
Examples: cubic close-packed and diamond structures
161(10)
The Representations of a Group in Terms of the Representations of an Invariant Subgroup
171(54)
Induced representations
171(5)
Groups with an invariant subgroup
176(5)
The theory of little groups
181(3)
The small representations of little groups
184(2)
The point groups as semi-direct products
186(15)
The reality of representations induced from little groups
201(3)
Direct products of induced representations
204(11)
Symmetrized and anti-symmetrized squares of induced representations
215(10)
The Single-Valued Representations of the 230 Space Groups
225(193)
Abstract groups
225(60)
The single-valued representations of the 230 space groups
285(104)
The labels of space-group representations
389(8)
Example of the use of the tables of the space-group representations
397(10)
Representation domain and basic domain
407(11)
The Double-Valued Representations of the 32 Point Groups and the 230 Space Groups
418(151)
The double-valued representations of the point groups
418(19)
Symmetry-adapted functions for double point groups
437(17)
The double-valued representations of the space groups
454(4)
An example of the deduction of the representations of a double space group
458(9)
The double-valued representations of the 230 space groups
467(102)
The Magnetic Groups and Their Corepresentations
569(113)
The Shubnikov groups and their derivation
569(1)
The classification of Shubnikov groups
570(35)
Anti-unitary operations and the corepresentations of magnetic groups
605(13)
The Kronecker products of corepresentations
618(4)
The corepresentations of the magnetic point groups
622(16)
The corepresentations of the magnetic space groups
638(14)
Example: the space-group corepresentations of P4'2/mnm' and their Kronecker products
652(17)
Spin-space groups
669(8)
Polychromatic point groups and space groups
677(5)
Appendix 682(2)
Bibliography 684(53)
Subject Index 737
Arthur P Cracknell graduated in Physics from the University of Cambridge in 1961, took his DPhil from the University of Oxford in 1964 and worked in the Physics Departments of the University of Singapore and the University of Essex before moving to Dundee as senior lecturer in 1970. He was promoted to Reader in 1974 and to Professor of Theoretical Physics in 1978 and later was transferred to the Carnegie Chair of Physics in the Department of Applied Physics and Electronic & Mechanical Engineering at Dundee University. He retired in 2002. He has won the Society Medal, The Remote Sensing Society, 1989; the Schiwefdsky Medal of the German Photogrammetric Society/ISPRS, 1996, and the President's award, Remote Sensing Society, 1996.



Christopher J Bradley won the Mayhew Prize for Distinction in Applied Mathematics, Cambridge, in 1959, before becoming Fellow in Applied Mathematics, Jesus College and CUF Lecturer in Mathematics, Oxford 1963-80. He later joined the teaching profession, and was Head of Mathematics, then Director of Studies, at Clifton College, Bristol, 1981-2003. He is a Fellow of the Institute of Mathematics and its Applications.