Ebook group theory and its applications in physics

Sales tax will be calculated at check-out. Free Global Shipping. Description 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. 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. This book has been written for physicists at an introductory level, keeping in view that a beginner will be able to understand the concepts relevant to the treatment of problems in physics.

Author : Eugene P. 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. In the second edition we have attempted to further clarify por tions of the text in reference to point symmetry, keeping certain sections and removing others.

The ever-expanding interest in solids necessitates some discussion on space symmetry. In this edition we have expanded the discus sion on point symmetry to include space symmetry. Numerous examples are pro vided to acquaint the reader with the procedure necessary to accomplish this. Recent examples from the literature are given to illustrate the use of group theory in the interpretation of molecular spectra and in the determination of molecular structure.

The text is intended for scientists and students with only a limited theoretical background in spectroscopy. For this reason we have presented detailed procedures for carrying out the selection rules and normal coor dinate treatment of molecules. We have chosen to exclude discussion on symmetry aspects of molecular orbital theory and ligand field theory. It has been our approach to highlight vibrational data only, primarily to keep the size and cost of the book to a reasonable limit.

The second edition of Group Theory for Chemists uses diagrams and problem-solving to help students test and improve their understanding, including a new section on the application of group theory to electronic spectroscopy. Part one covers the essentials of symmetry and group theory, including symmetry, point groups and representations.

Part two deals with the application of group theory to vibrational spectroscopy, with chapters covering topics such as reducible representations and techniques of vibrational spectroscopy. In part three, group theory as applied to structure and bonding is considered, with chapters on the fundamentals of molecular orbital theory, octahedral complexes and ferrocene among other topics.

Additionally in the second edition, part four focuses on the application of group theory to electronic spectroscopy, covering symmetry and selection rules, terms and configurations and d-d spectra. Provides a focused and comprehensive study of group theory and its applications, an invaluable resource to students of chemistry as well as those in related fields seeking an introduction to the topic Presents diagrams and problem-solving exercises to help students improve their understanding, including a new section on the application of group theory to electronic spectroscopy Reviews the essentials of symmetry and group theory, including symmetry, point groups and representations and the application of group theory to vibrational spectroscopy.

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Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems.

The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy.

The selection is a dependable reference for physicists and chemists interested in group theory and its applications. Introduction II. Preliminary Survey III. Direct Integrals of Representations V. Murray-von Neumann Typology VI. Inducing for Locally Compact Groups X.