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Author: Shoon K. Kim
Publisher: Cambridge University Press
Published: 1999-06-24
Total Pages: 512
ISBN-13: 0521640628
DOWNLOAD EBOOKFrom the pioneering author in the field, this book is ideal for condensed matter physicists and physical chemists.
Author: Thomas Wolfram
Publisher: Cambridge University Press
Published: 2014-01-09
Total Pages: 485
ISBN-13: 1107028523
DOWNLOAD EBOOKAn applications-oriented approach gives graduate students and researchers in the physical sciences the tools needed to analyze any physical system.
Author: Mildred S. Dresselhaus
Publisher: Springer Science & Business Media
Published: 2007-12-18
Total Pages: 576
ISBN-13: 3540328998
DOWNLOAD EBOOKThis 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: M. I. Petrashen
Publisher: Courier Corporation
Published: 2013-01-03
Total Pages: 338
ISBN-13: 0486172724
DOWNLOAD EBOOKGeared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.
Author: Robert A. Evarestov
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 292
ISBN-13: 3642604889
DOWNLOAD EBOOKSite 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: Nikolai B. Melnikov
Publisher: Springer Nature
Published: 2023-01-01
Total Pages: 343
ISBN-13: 3031139917
DOWNLOAD EBOOKThis 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.
Author: M.A. Markov
Publisher: CRC Press
Published: 2024-11-15
Total Pages: 673
ISBN-13: 1040284477
DOWNLOAD EBOOKThese Proceedings cover various topics in modern physics in which group theoretical methods can be applied effectively. The two volumes, containing over 100 papers, cover such areas as representation theory, the theory and applications of dynamical symmetries and coherent states, symmetries in atomic, molecular, nuclear and elementary particle physics, field theory including gauge theories, supersymmetry and supergravity, general relativity and cosmology, the theory of space groups and its applications to solid state physics and phase transitions, the problems of quantum and classical mechanics and paraxial optics, and the theory of nonlinear equations and solitons.
Author: Wolfram Hergert
Publisher: John Wiley & Sons
Published: 2018-08-20
Total Pages: 387
ISBN-13: 352741133X
DOWNLOAD EBOOKWhile 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: Chi-Sing Man
Publisher: Springer Nature
Published: 2023-01-13
Total Pages: 438
ISBN-13: 9402421580
DOWNLOAD EBOOKThis book starts with an introduction to quantitative texture analysis (QTA), which adopts conventions (active rotations, definition of Euler angles, Wigner D-functions) that conform to those of the present-day mathematics and physics literature. Basic concepts (e.g., orientation; orientation distribution function (ODF), orientation density function, and their relationship) are made precise through their mathematical definition. Parts II and III delve deeper into the mathematical foundations of QTA, where the important role played by group representations is emphasized. Part II includes one chapter on generalized QTA based on the orthogonal group, and Part III one on tensorial Fourier expansion of the ODF and tensorial texture coefficients. This work will appeal to students and practitioners who appreciate a precise presentation of QTA through a unifying mathematical language, and to researchers who are interested in applications of group representations to texture analysis. Previously published in the Journal of Elasticity, Volume 149, issues 1-2, April, 2022
Author: Jorge Kohanoff
Publisher: Cambridge University Press
Published: 2006-06-29
Total Pages: 372
ISBN-13: 1139453483
DOWNLOAD EBOOKElectronic structure problems are studied in condensed matter physics and theoretical chemistry to provide important insights into the properties of matter. This 2006 graduate textbook describes the main theoretical approaches and computational techniques, from the simplest approximations to the most sophisticated methods. It starts with a detailed description of the various theoretical approaches to calculating the electronic structure of solids and molecules, including density-functional theory and chemical methods based on Hartree-Fock theory. The basic approximations are thoroughly discussed, and an in-depth overview of recent advances and alternative approaches in DFT is given. The second part discusses the different practical methods used to solve the electronic structure problem computationally, for both DFT and Hartree-Fock approaches. Adopting a unique and open approach, this textbook is aimed at graduate students in physics and chemistry, and is intended to improve communication between these communities. It also serves as a reference for researchers entering the field.
