Problems & Solutions in Group Theory for Physicists

Author: Zhong-Qi Ma,Xiao-Yan Gu
Publisher: World Scientific
ISBN: 9789812388339
Category: Science
Page: 464
View: 4043

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This book is aimed at graduate students and young researchers in physics who are studying group theory and its application to physics. It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory. This book is also suitable for some graduate students in theoretical chemistry.

Group Theory in Physics

Problems and Solutions
Author: Michael Aivazis
Publisher: World Scientific
ISBN: 9789810204860
Category: Science
Page: 111
View: 7266

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This solutions booklet is a supplement to the text book 'Group Theory in Physics' by Wu-Ki Tung. It will be useful to lecturers and students taking the subject as detailed solutions are given.

Group Theory for Physicists

Author: Zhongqi Ma
Publisher: World Scientific
ISBN: 9812771417
Category: Science
Page: 491
View: 5180

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This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Application methods to physics are emphasized. New materials drawn from the teaching and research experience of the author are included. This book can be used by graduate students and young researchers in physics, especially theoretical physics. It is also suitable for some graduate students in theoretical chemistry.

Elements of Group Theory for Physicists

Author: A. W. Joshi
Publisher: New Age International
ISBN: 9788122409758
Category: Group theory
Page: 305
View: 6659

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The Mathematical Study Of Group Theory Was Initiated In The Early Nineteenth Century By Such Mathematicians As Gauss, Cauchy, Abel, Hamilton, Galois, Cayley, And Many Others. However, The Advantages Of Group Theory In Physics Were Not Recognized Till 1925 When It Was Applied For Formal Study Of Theoretical Foundations Of Quantum Mechanics, Atomic Structures And Spectra By, To Name A Few, H A Bethe, E P Wigner, Etc. It Has Now Become Indispensable In Several Branches Of Physics And Physical Chemistry.Dr. Joshi Develops The Mathematics Of Group Theory And Then Goes On To Present Its Applications To Quantum Mechanics, Crystallography, And Solid State Physics. For Proper Comprehension Of Representation Theory, He Has Covered Thoroughly Such Diverse But Relevant Topics As Hilbert Spaces, Function Spaces, Operators, And Direct Sum And Product Of Matrices. He Often Proceeds From The Particular To The General So That The Beginning Student Does Not Have An Impression That Group Theory Is Merely A Branch Of Abstract Mathematics. Various Concepts Have Been Explained Consistently By The Use Of The C4V. Besides, It Contains An Improved And More General Proof Of The Schurs First Lemma And An Interpretation Of The Orthogonality Theorem In The Language Of Vector Spaces (Chapter 3).Throughout The Text The Author Gives Attention To Details And Avoids Complicated Notation. This Is A Valuable Book For Senior Students And Researchers In Physics And Physical Chemistry. A Thorough Understanding Of The Methodology And Results Contained In This Book Will Provide The Reader Sound Theoretical Foundations For Advanced Study Of Quantum Mechanics, Solid State Physics And Atomic And Particle Physics To Help Students A Flow-Chart Explaining Step By Step The Method Of Determining A Parallel-Running Example Illustrating The Procedure In Full Details Have Been Included. An Appendix On Mappings And Functions Has Also Been Added.

Group Theory and Its Application to Physical Problems

Author: Morton Hamermesh
Publisher: Courier Corporation
ISBN: 0486140393
Category: Science
Page: 544
View: 7353

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One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.

Problems and Solutions in Quantum Chemistry and Physics

Author: Charles S. Johnson,Lee G. Pedersen
Publisher: Courier Corporation
ISBN: 0486151530
Category: Science
Page: 448
View: 7268

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Unusually varied problems, with detailed solutions, cover quantum mechanics, wave mechanics, angular momentum, molecular spectroscopy, scattering theory, more. 280 problems, plus 139 supplementary exercises.

Problems & Solutions in Theoretical & Mathematical Physics: Advanced level

Author: Willi-Hans Steeb
Publisher: World Scientific
ISBN: 9789812389879
Category: Science
Page: 362
View: 8775

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This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.

Symmetries and Conservation Laws in Particle Physics

An Introduction to Group Theory for Particle Physicists
Author: Stephen Haywood
Publisher: World Scientific
ISBN: 1848167032
Category: Science
Page: 152
View: 2276

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This book will explain how group theory underpins some of the key features of particle physics. It will examine symmetries and conservation laws in quantum mechanics and relate these to groups of transformations. Group theory provides the language for describing how particles (and in particular, their quantum numbers) combine. This provides understanding of hadronic physics as well as physics beyond the Standard Model. The symmetries of the Standard Model associated with the Electroweak and Strong (QCD) forces are described by the groups U(1), SU(2) and SU(3). The properties of these groups are examined and the relevance to particle physics is discussed.Stephen Haywood, author of Symmetries And Conservation Laws In Particle Physics, explains how his book can help experimental physicists and PhD students understand group theory and particle physics in our new video!View the interview at http: //

Group Theory in Solid State Physics and Photonics

Problem Solving with Mathematica
Author: Wolfram Hergert,Christian Matyssek,R. Matthias Geilhufe
Publisher: John Wiley & Sons
ISBN: 352741133X
Category: Science
Page: 377
View: 876

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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.

Problems and Solutions in Introductory and Advanced Matrix Calculus

Author: W.-H. Steeb,Willi-Hans Steeb
Publisher: World Scientific
ISBN: 9812569162
Category: Science
Page: 239
View: 2572

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As an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students. The coverage includes systems of linear equations, linear differential equations, functions of matrices and the Kronecker product. Many of the problems are related to applications in areas such as group theory, Lie algebra theory and graph theory. Thus, physics and engineering students will also benefit from the book. Exercises for matrix-valued differential forms are also included.

Problems and Solutions in Introductory and Advanced Matrix Calculus

Second Edition
Author: Willi-Hans Steeb,Yorick Hardy
Publisher: World Scientific Publishing Company
ISBN: 9813143819
Category: Mathematics
Page: 568
View: 5571

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This book provides an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus. Supplementary problems in each chapter will challenge and excite the reader, ideal for both graduate and undergraduate mathematics and theoretical physics students. The coverage includes systems of linear equations, linear differential equations, integration and matrices, Kronecker product and vec-operation as well as functions of matrices. Furthermore, specialized topics such as spectral theorem, nonnormal matrices and mutually unbiased bases are included. Many of the problems are related to applications for group theory, Lie algebra theory, wavelets, graph theory and matrix-valued differential forms, benefitting physics and engineering students and researchers alike. It also branches out to problems with tensors and the hyperdeterminant. Computer algebra programs in Maxima and SymbolicC++ have also been provided.

Group Theory

Application to the Physics of Condensed Matter
Author: Mildred S. Dresselhaus,Gene Dresselhaus,Ado Jorio
Publisher: Springer Science & Business Media
ISBN: 3540328971
Category: Science
Page: 582
View: 9973

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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.

Mathematical Tools for Physicists

Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 3527684271
Category: Science
Page: 632
View: 5328

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The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Groups, Representations and Physics

Author: H.F Jones
Publisher: CRC Press
ISBN: 9781420050295
Category: Mathematics
Page: 340
View: 4653

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Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Applications of Group Theory in Physics and Mathematical Physics

Author: MoshŽ Flato,Paul Sally,Gregg Zuckerman
Publisher: American Mathematical Soc.
ISBN: 9780821896860
Category: Science
Page: 420
View: 9571

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The past decade has seen a renewal in the close ties between mathematics and physics. The Chicago Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, held in July, 1982, was organized to bring together a broad spectrum of scientists from theoretical physics, mathematical physics, and various branches of pure and applied mathematics in order to promote interaction and an exchange of ideas and results in areas of common interest. This volume contains the papers submitted by speakers at the Seminar. The reader will find several groups of articles varying from the most abstract aspects of mathematics to a concrete phenomenological description of some models applicable to particle physics. The papers have been divided into four categories corresponding to the principal topics covered at the Seminar. This is only a rough division, and some papers overlap two or more of these categories.

Symmetries and Group Theory in Particle Physics

An Introduction to Space-Time and Internal Symmetries
Author: Giovanni Costa,Gianluigi Fogli
Publisher: Springer Science & Business Media
ISBN: 3642154816
Category: Science
Page: 291
View: 7136

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Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.

Compendium to Radiation Physics for Medical Physicists

300 Problems and Solutions
Author: Ervin B. Podgorsak
Publisher: Springer Science & Business Media
ISBN: 3642201865
Category: Science
Page: 1148
View: 1343

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This exercise book contains 300 typical problems and exercises in modern physics and radiation physics with complete solutions, detailed equations and graphs. This textbook is linked directly with the textbook "Radiation Physics for Medical Physicists", Springer (2010) but can also be used in combination with other related textbooks. For ease of use, this textbook has exactly the same organizational layout (14 chapters, 128 sections) as the "Radiation Physics for Medical Physicists" textbook and each section is covered by at least one problem with solution given. Equations, figures and tables are cross-referenced between the two books. It is the only large compilation of textbook material and associated solved problems in medical physics, radiation physics, and biophysics.

Theory of Groups and Its Application to Physical Problems

Author: S. Bhagavantam,T. Venkatarayudu
Publisher: Academic Press
ISBN: 1483275981
Category: Science
Page: 294
View: 5369

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Theory of Groups and Its Application to Physical Problems is an introductory study of the theory of groups for persons with no easy access to an orthodox mathematical treatise on the subject. The aim is to provide an understanding of the method of applying group theory to various problems and appreciate the advantages thereof. It is hoped that this account of the theory of groups will serve a real need for physicists interested in the subject. The book opens with a discussion of the concept of groups. This is followed by separate chapters on the one-dimensional and two-dimensional lattices, some properties of groups, matrix groups, and the wave equation and its properties. Subsequent chapters deal with vibrations of a dynamical system, vibrational Raman effect and infrared absorption, molecular structure and normal modes, three-dimensional lattices, Raman and infrared spectra of crystals, crystal symmetry and physical properties, rotation groups, and applications to problems of atomic spectra.