The Mathematical Theory of Symmetry in Solids PDF Download
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Author: Christopher Bradley
Publisher: Oxford University Press
ISBN: 0199582580
Category : Mathematics
Languages : en
Pages : 758
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Book Description
This classic book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.
Author: Christopher Bradley
Publisher: Oxford University Press
ISBN: 0199582580
Category : Mathematics
Languages : en
Pages : 758
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Book Description
This classic book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.
Author: Christopher John Bradley
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: William John Ibbetson
Publisher:
ISBN:
Category : Curvilinear coordinates
Languages : en
Pages : 548
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Book Description
Author: István Hargittai
Publisher: Elsevier
ISBN: 1483149528
Category : Science
Languages : en
Pages : 1060
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Book Description
International Series in Modern Applied Mathematics and Computer Science, Volume 10: Symmetry: Unifying Human Understanding provides a tremendous scope of “symmetry , covering subjects from fractals through court dances to crystallography and literature. This book discusses the limits of perfection, symmetry as an aesthetic factor, extension of the Neumann-Minnigerode-Curie principle, and symmetry of point imperfections in solids. The symmetry rules for chemical reactions, matching and symmetry of graphs, mosaic patterns of H. J. Woods, and bilateral symmetry in insects are also elaborated. This text likewise covers the crystallographic patterns, Milton's mathematical symbol of theodicy, symmetries of soap films, and gapon formalism. This volume is a good source for researchers and specialists concerned with symmetry.
Author: S. J. Joshua
Publisher: CRC Press
ISBN: 9780750300711
Category : Science
Languages : en
Pages : 288
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Book Description
Group theory and symmetry are important concepts in solid state physics, but are not widely taught because of the mathematical complexities involved. This book aims to remedy this by using a practical approach which bypasses most of the abstruse detail of formal group theory. The subject is usually developed using abstract entities, but here the author uses concrete examples to aid understanding in his development of the basics of the subject. This makes the book an ideal text for senior undergraduate and graduate students. The book is divided into two parts. Part one introduces the reader to group theoretical techniques and applications via the extensive use of character tables. All topics required for a complete understanding of group theory in the context of solid state physics are covered. The author demonstrates clearly how symmetry arguments can be applied to give detailed insights into the physical properties of crystals. This part ends with a selection of applications which will prove useful to solid state physicists/chemists and materials scientists. Each chapter includes a set of problems with hints and solutions. Part two is self-contained and deals with applications of group theory to the study of the symmetry properties of strongly magnetic crystals. This is a topic usually omitted from group theory texts at this level. Symmetry Principles and Magnetic Symmetry in Solid State Physics is a comprehensive introduction to the subject. It will be of great use to all students of condensed matter and materials science.
Author: Wolfgang Ludwig
Publisher: Springer Science & Business Media
ISBN: 3642799779
Category : Science
Languages : en
Pages : 488
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Book Description
Symmetries in Physics presents the fundamental theories of symmetry, together with many examples of applications taken from several different branches of physics. Emphasis is placed on the theory of group representations and on the powerful method of projection operators. The excercises are intended to stimulate readers to apply the techniques demonstrated in the text.
Author: J. L. Birman
Publisher: Springer Science & Business Media
ISBN: 3642697070
Category : Science
Languages : en
Pages : 558
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Book Description
Reissue of Encyclopedia of Physics/Handbuch der Physik, Vol. XXV/2b I am very pleased that my book is now to be reprinted and rebound in a new format which should make it accessible at a modest price to students and active researchers in condensed matter physics. In writing this book I had in mind an audience of physicists and chemists with no previous deep exposure to symmetry analysis of crystalline matter, non to the use of symmetry in simplifying and refining predictions of the results of optical experiments. Hence the book was written to explain and illustrate in all necessary detail how to: 1) describe the space group symmetry in terms of space group symmetry operations; 2) obtain irreducible representations and selection rules for optical infra-red and Raman and other transition processes. On the physical side I redeveloped the traditional theory of classical and quantum lattice dynamics, illustrating how space-time symmetry designations in the equations of motion can: 1) simplify and rationalize calculations of the classical eigenvectors of the dynamical equation; 2) permit classification of the eigenstates of the quantum lattice-dynamic pro blem; 3) give specific selection rules for optical infra-red and Raman lattice processes, and thus make "go, no-go" predictions including polarization of absorbed or scattered radiation; and 4) simplify the modern many-body theories of optical processes.
Author: Wolfram Hergert
Publisher: John Wiley & Sons
ISBN: 3527413014
Category : Science
Languages : en
Pages : 360
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Book Description
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
Author: Gideon Gilat
Publisher: Elsevier
ISBN: 032315008X
Category : Science
Languages : en
Pages : 444
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Book Description
Methods in Computational Physics, Volume 15: Vibrational Properties of Solids explores the application of computational methods to delineate microscopic vibrational behavior. This book is composed of nine chapters that further illustrate the utility of these methods to ordered lattices, quantum solids, impurity modes, surface modes, and amorphous solids. The opening chapters present the basic theoretical models and their computational aspects for different solids of diverse chemical nature, together with some methods of automation and computation in the highly sophisticated experiments in inelastic scattering of neutrons. These topics are followed by a discussion on how group theoretical methods treated by computers can yield the proper symmetry assignments of phonon eigenvalues and eigenstates. Considerable chapters are devoted to the different applications of traditional lattice dynamics, each having its own computational ramification. Other chapters survey the properties of solids that mostly involve integrations over the Brillouin zone. The last chapter concerns the dynamic or time-dependent aspect of lattice dynamics, namely, the calculation of thermal and electric conductivities in some models of solids. This book is of great benefit to geoscientists, physicists, and mathematicians.
Author: Tianyou Fan
Publisher: Springer Science & Business Media
ISBN: 3642146430
Category : Science
Languages : en
Pages : 350
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Book Description
This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.
