# Group Theory And Quantum Mechanics

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## Group Theory and Quantum Mechanics

Author | : Michael Tinkham |

Publsiher | : Courier Corporation |

Total Pages | : 354 |

Release | : 2012-04-20 |

ISBN | : 0486131661 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Group Theory and Quantum Mechanics Book Excerpt:**

This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids. The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

## Group Theory and Quantum Mechanics

Author | : Bartel L. van der Waerden |

Publsiher | : Springer Science & Business Media |

Total Pages | : 211 |

Release | : 2012-12-06 |

ISBN | : 3642658601 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Theory and Quantum Mechanics Book Excerpt:**

The German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.

## Applications of Group Theory in Quantum Mechanics

Author | : M. I. Petrashen,J. L. Trifonov |

Publsiher | : Courier Corporation |

Total Pages | : 336 |

Release | : 2013-01-03 |

ISBN | : 0486172724 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Applications of Group Theory in Quantum Mechanics Book Excerpt:**

This advanced text explores the theory of groups and their matrix representations. The main focus rests upon point and space groups, with applications to electronic and vibrational states. 1969 edition.

## Group Theory

Author | : Eugene P. Wigner |

Publsiher | : Elsevier |

Total Pages | : 384 |

Release | : 2013-09-03 |

ISBN | : 1483275760 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Group Theory Book Excerpt:**

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.

## The Theory of Groups and Quantum Mechanics

Author | : Hermann Weyl |

Publsiher | : Courier Corporation |

Total Pages | : 422 |

Release | : 1950-01-01 |

ISBN | : 9780486602691 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**The Theory of Groups and Quantum Mechanics Book Excerpt:**

This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

## A Course on the Application of Group Theory to Quantum Mechanics

Author | : Irene Verona Schensted |

Publsiher | : Neo Press |

Total Pages | : 342 |

Release | : 1976 |

ISBN | : 1928374650XXX |

Category | : Física matemática |

Language | : EN, FR, DE, ES & NL |

**A Course on the Application of Group Theory to Quantum Mechanics Book Excerpt:**

## Group Theory in Quantum Mechanics

Author | : Volker Heine |

Publsiher | : Elsevier |

Total Pages | : 478 |

Release | : 2014-05-15 |

ISBN | : 1483152006 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Group Theory in Quantum Mechanics Book Excerpt:**

Group Theory in Quantum Mechanics: An Introduction to its Present Usage introduces the reader to the three main uses of group theory in quantum mechanics: to label energy levels and the corresponding eigenstates; to discuss qualitatively the splitting of energy levels as one starts from an approximate Hamiltonian and adds correction terms; and to aid in the evaluation of matrix elements of all kinds, and in particular to provide general selection rules for the non-zero ones. The theme is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions. This book is comprised of eight chapters and begins with an overview of the necessary mathematical concepts, including representations and vector spaces and their relevance to quantum mechanics. The uses of symmetry properties and mathematical expression of symmetry operations are also outlined, along with symmetry transformations of the Hamiltonian. The next chapter describes the three uses of group theory, with particular reference to the theory of atomic energy levels and transitions. The following chapters deal with the theory of free atoms and ions; representations of finite groups; the electronic structure and vibrations of molecules; solid state physics; and relativistic quantum mechanics. Nuclear physics is also discussed, with emphasis on the isotopic spin formalism, nuclear forces, and the reactions that arise when the nuclei take part in time-dependent processes. This monograph will be of interest to physicists and mathematicians.

## Applications of Group Theory in Quantum Mechanics

Author | : M. I. Petrashen,E. D. Trifonov,S. Chomet |

Publsiher | : Courier Corporation |

Total Pages | : 318 |

Release | : 2009-03-01 |

ISBN | : 048647223X |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Applications of Group Theory in Quantum Mechanics Book Excerpt:**

Geared toward theoretical physicists, this advanced text explores the value of modern group-theoretical methods in quantum theory. It explains the theory of groups and their matrix representations, developing them to the level required for applications. The main focus rests upon point and space groups, with applications to electronic and vibrational states. 1969 edition.

## Elements of Group Theory for Physicists

Author | : A. W. Joshi |

Publsiher | : New Age International |

Total Pages | : 305 |

Release | : 1997 |

ISBN | : 9788122409758 |

Category | : Group theory |

Language | : EN, FR, DE, ES & NL |

**Elements of Group Theory for Physicists Book Excerpt:**

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 |

Publsiher | : Courier Corporation |

Total Pages | : 509 |

Release | : 1989-01-01 |

ISBN | : 9780486661810 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Group Theory and Its Application to Physical Problems Book Excerpt:**

"A remarkably intelligible survey . . . well organized, well written and very clear throughout." — Mathematical Reviews This excellent text, long considered one of the best-written, most skillful expositions of group theory and its physical applications, is directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. No knowledge of group theory is assumed, but the reader is expected to be familiar with quantum mechanics. And while much of the book concerns theory, readers will nevertheless find a large number of physical applications in the fields of crystallography, molecular theory, and atomic and nuclear physics. The first seven chapters of the book are concerned with finite groups, focusing on the central role of the symmetric group. This section concludes with a chapter dealing with the problem of determining group characters, as it discusses Young tableaux, Yamanouchi symbols, and the method of Hund. The remaining five chapters discuss continuous groups, particularly Lie groups, with the final chapter devoted to the ray representation of Lie groups. The author, Professor Emeritus of Physics at the University of Minnesota, has included a generous selection of problems. They are inserted throughout the text at the place where they naturally arise, making the book ideal for self-study as well as for classroom assignment. 77 illustrations. "A very welcome addition to [the] literature. . . . I would warmly recommend the book to all serious students of Group Theory as applied to Physics." — Contemporary Physics. Index. Bibliography. Problems. Tables.

## Group Theory and Physics

Author | : S. Sternberg |

Publsiher | : Cambridge University Press |

Total Pages | : 429 |

Release | : 1995-09-07 |

ISBN | : 9780521558853 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Theory and Physics Book Excerpt:**

A cohesive and well-motivated introduction to group theory and its application to physics.

## The Collected Works of Eugene Paul Wigner

Author | : Eugene Paul Wigner |

Publsiher | : Springer Science & Business Media |

Total Pages | : 536 |

Release | : 2001-09-11 |

ISBN | : 9783540572947 |

Category | : Language Arts & Disciplines |

Language | : EN, FR, DE, ES & NL |

**The Collected Works of Eugene Paul Wigner Book Excerpt:**

Not only was E.P. Wigner one of the most active creators of 20th century physics, he was also always interested in expressing his opinion in philosophical, political or sociological matters. This volume of his collected works covers a wide selection of his essays about science and society, about himself and his colleagues. Annotated by J. Mehra, this volume will become an important source of reference for historians of science, and it will be pleasant reading for every physicist interested in forming ideas in modern physics.

## Group Theory in Physics

Author | : Wu-Ki Tung |

Publsiher | : World Scientific |

Total Pages | : 344 |

Release | : 1985 |

ISBN | : 9971966565 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Group Theory in Physics Book Excerpt:**

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet.

## Lie Groups and Quantum Mechanics

Author | : D. J. Simms |

Publsiher | : Springer Verlag |

Total Pages | : 90 |

Release | : 1968 |

ISBN | : 1928374650XXX |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Lie Groups and Quantum Mechanics Book Excerpt:**

## Group Theory in Physics

Author | : Wu-Ki Tung |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 336 |

Release | : 1985-08-31 |

ISBN | : 981310404X |

Category | : Representations of groups |

Language | : EN, FR, DE, ES & NL |

**Group Theory in Physics Book Excerpt:**

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy

## Problems and Solutions in Group Theory for Physicists

Author | : Zhong-Qi Ma,Xiao-Yan Gu |

Publsiher | : World Scientific |

Total Pages | : 476 |

Release | : 2004-06-04 |

ISBN | : 9814482765 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Problems and Solutions in Group Theory for Physicists Book Excerpt:**

' This book is aimed at graduate students 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. The 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. Contents:Review on Linear AlgebrasGroup and Its SubsetsTheory of RepresentationsThree-Dimensional Rotation GroupSymmetry of CrystalsPermutation GroupsLie Groups and Lie AlgebrasUnitary GroupsReal Orthogonal GroupsThe Symplectic Groups Keywords:Group Theory;Problems and Solutions;Exercises;Theory of Angular Momentum;Finite Group;Symmetry Group of Polyhedron;Space Groups;Permutation Group;Young Operator;Lie Group;Lie AlgebraReviews:“The authors present an interesting book explaining group theory in terms of physics, closing an often observed gap in the literature between abstract mathematical theory and physical applications … It is self-contained as much as is possible. Many examples and exercises, including solutions, allow the reader to become more familiar with the subject.”Mathematical Reviews '

## Symmetries and Group Theory in Particle Physics

Author | : Giovanni Costa,Gianluigi Fogli |

Publsiher | : Springer Science & Business Media |

Total Pages | : 291 |

Release | : 2012-02-05 |

ISBN | : 3642154816 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Symmetries and Group Theory in Particle Physics Book Excerpt:**

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.

## Group Theory for Physicists

Author | : Zhongqi Ma |

Publsiher | : World Scientific |

Total Pages | : 491 |

Release | : 2007 |

ISBN | : 9812771417 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Group Theory for Physicists Book Excerpt:**

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.

## An Introduction to Tensors and Group Theory for Physicists

Author | : Nadir Jeevanjee |

Publsiher | : Birkhäuser |

Total Pages | : 305 |

Release | : 2015-03-11 |

ISBN | : 3319147943 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**An Introduction to Tensors and Group Theory for Physicists Book Excerpt:**

The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews

## Group Theory

Author | : R. Mirman |

Publsiher | : World Scientific |

Total Pages | : 492 |

Release | : 1995 |

ISBN | : 9789810233655 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Theory Book Excerpt:**

A thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.