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: Ulrich Müller
Publisher: Academic
ISBN: 0199669953
Category : Science
Languages : en
Pages : 349
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Book Description
The book presents the basic information needed to understand and to organize the huge amount of known structures of crystalline solids. Its basis is crystallographic group theory (space group theory), with special emphasis on the relations between the symmetry properties of crystals.
Author: Simon L. Altmann
Publisher: Oxford University Press, USA
ISBN:
Category : History
Languages : en
Pages : 312
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Book Description
The structure of much of solid-state theory comes directly from group theory, but until now there has been no elementary introduction to the band theory of solids using this approach. Employing the most basic of group theoretical ideas, and emphasizing the significance of symmetry in determining many of the essential concepts, this is the only book to provide such an introduction. Many topics were chosen with the needs of chemists in mind, and numerous problems are included to enable the reader to apply the major ideas and to complete some parts of the treatment. Physical scientists will also find this a valuable introduction to the field.
Author: Kristopher Tapp
Publisher: Springer Nature
ISBN: 3030516695
Category : Mathematics
Languages : en
Pages : 263
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Book Description
This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.
Author: Mildred S. Dresselhaus
Publisher: Springer Science & Business Media
ISBN: 3540328998
Category : Science
Languages : en
Pages : 576
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Book Description
This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.
Author: Robert A. Evarestov
Publisher: Springer Science & Business Media
ISBN: 3642604889
Category : Science
Languages : en
Pages : 292
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Book Description
Site Symmetry in Crystals is the first comprehensive account of the group-theoretical aspects of the site (local) symmetry approach to the study of crystalline solids. The efficiency of this approach, which is based on the concepts of simple induced and band representations of space groups, is demonstrated by considering newly developed applications to electron surface states, point defects, symmetry analysis in lattice dynamics, the theory of second-order phase transitions, and magnetically ordered and non-rigid crystals. Tables of simple induced respresentations are given for the 24 most common space groups, allowing the rapid analysis of electron and phonon states in complex crystals with many atoms in the unit cell.
Author: Wolfgang Ludwig
Publisher: Springer Science & Business Media
ISBN: 364297029X
Category : Science
Languages : en
Pages : 471
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Book Description
Everyone knows that symmetry is fundamentally important in physics. On one hand, the symmetry of a system is often the starting point for general physical considerations, and on the other hand, particular problems may be solved in simpler and more elegant ways if symmetry is taken into account. This book presents the underlying theories of symmetry and gives examples of their application in branches of physics ranging from solid-state to high-energy physics via atomic and molecular physics. The text is as self-contained as possible, with as much mathematical formalism given as required. The main emphasis is on the theory of group representations and on the method of projection operators, this is a very powerful tool which is often treated only very briefly. Discrete symmetries, continuous symmetries and symmetry breaking are also discussed, and exercises are provided to stimulate the reader to carry out original work.
Author: Michael Glazer
Publisher: Academic Press
ISBN: 0123946158
Category : Science
Languages : en
Pages : 423
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Book Description
This comprehensively revised – essentially rewritten – new edition of the 1990 edition (described as "extremely useful" by MATHEMATICAL REVIEWS and as "understandable and comprehensive" by Scitech) guides readers through the dense array of mathematical information in the International Tables Volume A. Thus, most scientists seeking to understand a crystal structure publication can do this from this book without necessarily having to consult the International Tables themselves. This remains the only book aimed at non-crystallographers devoted to teaching them about crystallographic space groups. - Reflecting the bewildering array of recent changes to the International Tables, this new edition brings the standard of science well up-to-date, reorganizes the logical order of chapters, improves diagrams and presents clearer explanations to aid understanding - Clarifies, condenses and simplifies the meaning of the deeply written, complete Tables of Crystallography into manageable chunks - Provides a detailed, multi-factor, interdisciplinary explanation of how to use the International Tables for a number of possible, hitherto unexplored uses - Presents essential knowledge to those needing the necessary but missing pedagogical support and detailed advice – useful for instance in symmetry of domain walls in solids
Author: Thomas Wolfram
Publisher: Cambridge University Press
ISBN: 1107028523
Category : Mathematics
Languages : en
Pages : 485
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Book Description
An applications-oriented approach gives graduate students and researchers in the physical sciences the tools needed to analyze any physical system.
Author: Nikolai B. Melnikov
Publisher: Springer Nature
ISBN: 3031139917
Category : Science
Languages : en
Pages : 343
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Book Description
This book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.
