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Author : Ernest M. Loebl
Publisher : Unknown
Page : 480 pages
File Size : 45,8 Mb
Release : 1975
Category : Electronic
ISBN : OCLC:760035032
Author : R. McWeeny
Publisher : Elsevier
Page : 262 pages
File Size : 45,7 Mb
Release : 2013-09-03
Category : Mathematics
ISBN : 9781483226248
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
Author : Ernest M. Loebl
Publisher : Academic Press
Page : 326 pages
File Size : 47,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483263786
Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger’s and Dirac’s for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.
Author : Teturo Inui,Yukito Tanabe,Yositaka Onodera
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642800214
This book has been written to introduce readers to group theory and its ap plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.
Author : M. Hamermesh
Publisher : Unknown
Page : 128 pages
File Size : 50,5 Mb
Release : 1964
Category : Electronic
ISBN : OCLC:841407509
Author : Mildred S. Dresselhaus,Gene Dresselhaus,Ado Jorio
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 54,5 Mb
Release : 2007-12-18
Category : Science
ISBN : 9783540328995
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 : Eugene P. Wigner
Publisher : Elsevier
Page : 384 pages
File Size : 53,6 Mb
Release : 2013-09-03
Category : Science
ISBN : 9781483275765
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with particular reference to atomic spectra. The manuscript first takes a look at vectors and matrices, generalizations, and principal axis transformation. Topics include principal axis transformation for unitary and Hermitian matrices; unitary matrices and the scalar product; linear independence of vectors; and real orthogonal and symmetric matrices. The publication also ponders on the elements of quantum mechanics, perturbation theory, and transformation theory and the bases for the statistical interpretation of quantum mechanics. The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of atomic spectra. Discussions focus on eigenvalues and quantum numbers, spherical harmonics, and representations of the unitary group. The manuscript is a valuable reference for readers interested in the applications of group theoretical methods.
Author : KUNJU, A. SALAHUDDIN,KRISHNAN, G.
Publisher : PHI Learning Pvt. Ltd.
Page : 296 pages
File Size : 44,7 Mb
Release : 2015-08-31
Category : Science
ISBN : 9788120351349
This book, divided into two parts, now in its second edition, presents the basic principles of group theory and their applications in chemical theories. While retaining the thorough coverage of the previous edition, the book in Part I, discusses the symmetry elements, point groups and construction of character tables for different point groups. In Part II, it describes the concept of hybridization to explain the shapes of molecules and analyzes the character tables to predict infrared and Raman active vibrational modes of molecules. It also brings into fore the molecular orbital theory and the techniques of group theory to interpret bonding in transition metal complexes and their electronic spectra. Finally, the book describes the crystal symmetry in detail as well as the Woodward–Hoffmann rules to determine the pathways of electrocyclic and cycloaddition reactions. NEW TO THE SECOND EDITION • New sections on Direct Product, Group–sub-group Relationships, Effect of Descent in Octahedral Symmetry on Degeneracy, Jahn–Teller Distortion, Group–sub-group Relationships and Electronic Spectra of Complexes and Influence of Coordination on the Infrared Spectra of Oxoanionic Ligands, Space Groups • Revised sections on Projection Operator, SALC Molecular Orbitals of Benzene and π-Molecular Orbitals of 1, 3-Butadiene KEY FEATURES • Provides mathematical foundations to understand group theory. • Includes several examples to illustrate applications of group theory. • Presents chapter-end exercises to help the students check their understanding of the subject matter. The book is designed for the senior undergraduate students and postgraduate students of Chemistry. It will also be of immense use to the researchers in the fields where group theory is applied.
Author : Gerald Burns
Publisher : Academic Press
Page : 446 pages
File Size : 41,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483191492
Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.
Author : Derek F. Holt,Bettina Eick,Eamonn A. O'Brien
Publisher : CRC Press
Page : 532 pages
File Size : 50,9 Mb
Release : 2005-01-13
Category : Mathematics
ISBN : 9781420035216
The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
Author : Patrick W. M. Jacobs
Publisher : Cambridge University Press
Page : 520 pages
File Size : 45,7 Mb
Release : 2005-10-18
Category : Mathematics
ISBN : 0521642507
This book provides a rigorous account on the fundamentals and applications of Group Theory to chemical physics.
Author : Petre P. Teodorescu,Nicolae-A.P. Nicorovici
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 40,7 Mb
Release : 2004-04-30
Category : Mathematics
ISBN : 9781402020476
The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.
Author : Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Publisher : CRC Press
Page : 188 pages
File Size : 42,8 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 9780203885765
Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state
Author : Grigoriĭ I︠A︡kovlevich Li︠u︡barskiĭ
Publisher : Reader's Digest Young Families
Page : 392 pages
File Size : 49,8 Mb
Release : 1960
Category : Mathematics
ISBN : MINN:31951000915716C
Elements of the theory of groups -- Some specific groups -- The theory of group representations -- Operations with group representations -- Representations of certain groups -- Small oscillations of symmetrical systems -- Second order phase transitions -- Crystals -- Infinite groups -- Representations of the rotation groups in two and three dimensions and of the full orthogonal group -- Clebsch-Gordon and Racah coefficients -- The Schrödinger equation -- Equations invariant under the Euclidean group of motions in space -- Absorption and Raman scattering of light -- Representations of the Lorentz group -- Relativistically invariant equations -- Nuclear reactions.
Author : John R. Ferraro,Joseph S. Ziomek
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461548218
This volume is a consequence of a series of seminars presented by the authors at the Infrared Spectroscopy Institute, Canisius College, Buffalo, New York, over the last nine years. Many participants on an intermediate level lacked a sufficient background in mathematics and quantum mechan ics, and it became evident that a non mathematical or nearly nonmathe matical approach would be necessary. The lectures were designed to fill this need and proved very successful. As a result of the interest that was developed in this approach, it was decided to write this book. The text is intended for scientists and students with only limited theore tical background in spectroscopy, but who are sincerely interested in the interpretation of molecular spectra. The book develops the detailed selection rules for fundamentals, combinations, and overtones for molecules in several point groups. Detailed procedures used in carrying out the normal coordinate treatment for several molecules are also presented. Numerous examples from the literature illustrate the use of group theory in the in terpretation of molecular spectra and in the determination of molecular structure.