Download or read book Spherical Tensor Operators Tables Of Matrix Elements And Symmetries written by Jack A Tuszynski and published by World Scientific. This book was released on 1990-08-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains introductory comments concerning the definitions, the symmetry properties and the basic formulae for matrix elements of tensor operators. The main body of text consists of tables of reduced matrix elements of double tensor operators within pn,dn and fn configurations, i.e. all the principal pure configurations of the atomic and nuclear structure. These tables are complete which means that the author has run through all the states of the following configurations: p2, p3, d2, d3, d4, d5, f2, f3, f4, f5, f6, f7 for multiparticle systems with central symmetry.Double tensor operators wk1k2 have been chosen in these calculations, for a number of reasons. First of all, they are the most general type of spherical tensor operators and, since they are normalized, they are the most convenient to use. Secondly, they have been very frequently used in many areas of physics, most notably in nuclear, atomic, molecular and solid state physics. There are also tabulated conversion factors to enable the use of these tables for other types of definitions of tensor operators.

Download or read book Spherical Tensor Operators written by J. A. Tuszynski and published by World Scientific. This book was released on 1990 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains introductory comments concerning the definitions, the symmetry properties and the basic formulae for matrix elements of tensor operators. The main body of text consists of tables of reduced matrix elements of double tensor operators within pn, dn and fn configurations, i.e. all the principal pure configurations of the atomic and nuclear structure. These tables are complete which means that the author has run through all the states of the following configurations: p2, p3, d2, d3, d4, d5, f2, f3, f4, f5, f6, f7 for multiparticle systems with central symmetry.Double tensor operators w1k2 have been chosen in these calculations, for a number of reasons. First of all, they are the most general type of spherical tensor operators and, since they are normalized, they are the most convenient to use. Secondly, they have been very frequently used in many areas of physics, most notably in nuclear, atomic, molecular and solid state physics. There are also tabulated conversion factors to enable the use of these tables for other types of definitions of tensor operators.

Download or read book Symmetry Broken Symmetry and Topology in Modern Physics written by Mike Guidry and published by Cambridge University Press. This book was released on 2022-03-31 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.

Download or read book Symmetry of Many Electron Systems written by I. G. Kaplan and published by Academic Press. This book was released on 2013-10-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry of Many-Electron Systems discusses the group-theoretical methods applied to physical and chemical problems. Group theory allows an individual to analyze qualitatively the elements of a certain system in scope. The text evaluates the characteristics of the Schrodinger equations. It is proved that some groups of continuous transformation from the Lie groups are useful in identifying conditions and in developing wavefunctions. A section of the book is devoted to the utilization of group-theoretical methods in quantal calculations on many-electron systems. The focus is on the use of group-theoretical methods to the classification and calculation of states of molecule. A chapter of the book gives a comprehensive discussion of the fractional parentage method. This application is used in atomic and nuclear spectroscopy. The method of employing coordinate wave functions is explained. The standard Young-Yamanouchi orthogonal representation is presented completely. The book will provide useful guides for physicists, chemists, engineers, students, and researchers in the field of physics.

Download or read book Molecular Structure and Statistical Thermodynamics written by Kenneth S. Pitzer and published by World Scientific. This book was released on 1993 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers molecular structural information, statistical methods and thermodynamic measurements, and the ways in which the relative role of each differs from another. By putting together selected papers in a single publication, the book highlights the cohesive aspects of certain advances through time and development, and can aid historical studies. Several papers from journals not widely circulated can also be found in this selection of papers.

Download or read book Symmetry Group Theory and the Physical Properties of Crystals written by Richard C Powell and published by Springer. This book was released on 2010-12-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complete with reference tables and sample problems, this volume serves as a textbook or reference for solid-state physics and chemistry, materials science, and engineering. Chapters illustrate symmetry, and its role in determining solid properties, as well as a demonstration of group theory.

Download or read book Angular Momentum in Quantum Mechanics written by A. R. Edmonds and published by Princeton University Press. This book was released on 2016-08-10 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.

Download or read book Rotational Structure in Molecular Infrared Spectra written by Carlo di Lauro and published by Elsevier. This book was released on 2020-05-17 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rotational Structure in Molecular Infrared Spectra, Second Edition, fills the gap between these complex topics and the most elementary methods in the field of rotational structure in the infrared spectra of gaseous molecules. Combining foundational theoretical information with advanced applications, this book is a useful guide for all those involved in the application of molecular spectroscopic techniques and the interpretation of vibration-rotation spectra. Interpreting vibration-rotation spectra is an important skill in many scientific disciplines, ranging from nanochemistry to planetary research, hence this book is an ideal resource. - Includes new content on the interaction of rotation and nuclear electric quadrupoles, coupled and uncoupled nuclei, and internal rotation from the high-barrier basis limit - Provides updated tables and figures throughout to support the knowledge outlined in the text - Outlines different paths through the text to help readers from different backgrounds explore the most appropriate content for their needs

Download or read book Point Group Symmetry Applications written by Philip H. Butler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical apparatus of group theory is a means of exploring and exploiting physical and algebraic structure in physical and chemical prob lems. The existence of structure in the physical processes leads to structure in the solutions. For group theory to be useful this structure need not be an exact symmetry, although as examples of exact symmetries we have that the identity of electrons leads to permutation symmetries in many-electron wave functions, the spatial structure of crystals leads to the Bloch theory of crystal eigenfunctions, and the rotational invariance of the hydrogenic Hamiltonian leads to its factorization into angular and radial parts. In the 1930's Wigner extended what is known to mathematicians as the theory of group representations and the theory of group algebras to study the coupling coefficients of angular momentum, relating various properties of the coefficients to the properties of the abstract group of rotations in 3-space. In 1949 Racah, in a paper on rare earth spectra, showed that similar coefficients occur in other situations. Immediately a number of studies of the coefficients were begun, notably by Jahn, with his applications in nuclear physics. In the years since then a large number of physicists and chemists have added to the development of a general theory of the coefficients, or have produced specialized tables for a specific application. Applications now range from high-energy physics to biology.

Download or read book Molecules in Physics Chemistry and Biology written by J. Maruani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1: General Introduction to Molecular Sciences Volume 2: Physical Aspects of Molecular Systems Volume 3: Electronic Structure and Chemical Reactivity Volume 4: Molecular Phenomena in Biological Sciences

Download or read book Multifrequency Electron Paramagnetic Resonance written by Sushil K. Misra and published by John Wiley & Sons. This book was released on 2014-03-19 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is aimed to deliver an up-to-date account of some of the recently developed experimental and theoretical methods in EPR, as well as a complete up-to-date listing of the experimentally determined values of multifrequency transition-ion spin Hamiltonian parameters by Sushil Misra, reported in the past 20 years, extending such a listing published by him in the Handbook on Electron Spin Resonance, volume 2. This extensive data tabulation makes up roughly 60% of the book`s content. It is complemented by the first full compilation of hyperfine splittings and g-factors for aminoxyl (nitroxide) radicals since 197 by Larry Berliner, a world expert on spin labeling, helping to identify and interpret substances and processes by means of EPR techniques. The book also includes coverage of the recently developed experimental technique of rapid-scan EPR by Sandra Eaton and Gareth Eaton, and a thorough review of computational modeling in EPR by Stefan Stoll, author of Easy Spin.

Download or read book Advances in Magnetic Resonance written by John S. Waugh and published by Academic Press. This book was released on 2013-10-22 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Magnetic Resonance, Volume 4 deals with the relaxation, irradiation, and other dynamical effects that is specific to systems having resolved structure in their magnetic resonance spectra. This book discusses the anisotropic rotation of molecules in liquids by NMR quadrupolar relaxation; rotational diffusion constants; alternating linewidth effect; and theoretical formulations of the problem. The line shapes in high-resolution NMR; matrix representations of the equations of motion; matrix representations of the equations of motion; and intramolecular hydrogen bonds are also deliberated. This text likewise covers the nuclear spin relaxation by double resonance and methods of solution of the density matrix equations. This publication is valuable to physics and chemistry students, including those interested in magnetic resonance.

Download or read book Molecular Symmetry and Spectroscopy written by Philip R. Bunker and published by NRC Research Press. This book was released on 2006 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition, by P.R. Bunker, published in 1979, remains the sole textbook that explains the use of the molecular symmetry group in understanding high resolution molecular spectra. Since 1979 there has been considerable progress in the field and a second edition is required; the original author has been joined in its writing by Per Jensen. The Material of the first edition has been reorganized and much has been added. The molecular symmetry group is now introduced early on, and the explanation of how to determine nuclear spin statistical weights has been consolidated in one chapter, after groups, symmetry groups, character tables and the Hamiltonian have been introduced. A description of the symmetry in the three-dimensional rotation group K(spatial), irreducible spherical tensor operators, and vector coupling coefficients is now included. The chapters on energy levels and selection rules contain a great deal of material that was not in the first edition (much of it was undiscovered in 1979), concerning the Jahn-Teller effect, the Renner effect, Multichannel Quantum Defect Theory, the use of variational methods for calculating rotational-vibration energy levels, and the contact transformed rotation-vibration Hamiltonian. A new chapter is devoted entirely to weakly bound cluster molecules (often called Van der Waals molecules). A selection of experimental spectra is included in order to illustrate particular theoretical points.

Download or read book High Magnetic Fields in Semiconductor Physics III written by Gottfried Landwehr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: High magnetic fields have, for a long time, been an important tool in the investigation of the electronic structure of semiconductors. In recent yearsstudies of heterostructures and superlattices have predominated, and this emphasis is reflected in these proceedings. The contributions concentrate on experiments using transport and optical methods, but recent theoretical developments are also covered. Special attention is paid to the quantum Hall effect, including the problem of edge currents, the influence of contacts, and Wigner condensation in the fractional quantum Hall effect regime. The 27 invited contributions by renowned expertsprovide an excellent survey of the field that is complemented by numerous contributed papers.

Download or read book Theoretical Foundations of Molecular Magnetism written by Roman Boča and published by Elsevier. This book was released on 1999-09-29 with total page 889 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetochemistry is a highly interdisciplinary field that attracts the interest of chemists, physicists and material scientists. Although the general strategy of theoretical molecular magnetism has been in place for decades, its performance for extended systems of interacting magnetic units can be very complicated. Professor Boca's book treats the "mosaic" of the theoretical approaches currently used in the field. This book presents a review of the theoretical concepts of molecular magnetism. The first chapter of the book recapitulates the necessary mathematical background. An overview of macroscopic magnetic properties is then presented. Formulation of magnetic parameters and methods of their calculation are given, followed by a brief summary of magnetic behaviour. The core of the book deals with the temperature dependence of magnetic susceptibility for mononuclear complexes, dimers, and exchange-coupled clusters.This book will be particularly useful for those scientists and students working in the field of molecular magnetism who need to refer to a complete and systematic treatment of the mathematics of magneto-chemical theory.

Download or read book Intermolecular Interactions written by Ilya G. Kaplan and published by John Wiley & Sons. This book was released on 2006-05-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book — intermolecular interactions — is as important in physics as in chemistry and molecular biology. Intermolecular interactions are responsible for the existence of liquids and solids in nature. They determine the physical and chemical properties of gases, liquids, and crystals, the stability of chemical complexes and biological compounds. In the first two chapters of this book, the detailed qualitative description of different types of intermolecular forces at large, intermediate and short-range distances is presented. For the first time in the monographic literature, the temperature dependence of the dispersion forces is discussed, and it is shown that at finite temperatures the famous Casimir-Polder asymptotic formula is correct only at narrow distance range. The author has aimed to make the presentation understandable to a broad scope of readers without oversimplification. In Chapter 3, the methods of quantitative calculation of the intermolecular interactions are discussed and modern achievements are presented. This chapter should be helpful for scientists performing computer calculations of many-electron systems. The last two chapters are devoted to the many-body effects and model potentials. More than 50 model potentials exploited for processing experimental data and computer simulation in different fields of physics, chemistry and molecular biology are represented. The widely used global optimisation methods: simulated annealing, diffusion equation method, basin-hopping algorithm, and genetic algorithm are described in detail. Significant efforts have been made to present the book in a self-sufficient way for readers. All the necessary mathematical apparatus, including vector and tensor calculus and the elements of the group theory, as well as the main methods used for quantal calculation of many-electron systems are presented in the appendices.

Download or read book The Interacting Boson Fermion Model written by F. Iachello and published by Cambridge University Press. This book was released on 1991-08-30 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interacting boson-fermion model has become in recent years the standard model for the description of atomic nuclei with an odd number of protons and/or neutrons. This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. The book addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed. The book is the first comprehensive treatment of the subject and will appeal to both theoretical and experimental physicists. The large number of explicit formulas for level energies, electromagnetic transition rates and intensities of transfer reactions presented in the book provide a simple but detailed way to analyse experimental data. This book can also be used as a textbook for advanced graduate students.