The Classical and Quantum 6j-symbols. (MN-43), Volume 43

The Classical and Quantum 6j-symbols. (MN-43), Volume 43
Author: J. Scott Carter
Publisher: Princeton University Press
Total Pages: 178
Release: 2021-08-10
Genre: Mathematics
ISBN: 0691234671
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Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals. The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.

Quantities, Units and Symbols in Physical Chemistry

Quantities, Units and Symbols in Physical Chemistry
Author: International Union of Pure and Applied Chemistry. Physical and Biophysical Chemistry Division
Publisher: Royal Society of Chemistry
Total Pages: 240
Release: 2007
Genre: Reference
ISBN: 0854044337
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Prepared by the IUPAC Physical Chemistry Division this definitive manual, now in its third edition, is designed to improve the exchange of scientific information among the readers in different disciplines and across different nations. This book has been systematically brought up to date and new sections added to reflect the increasing volume of scientific literature and terminology and expressions being used. The Third Edition reflects the experience of the contributors with the previous editions and the comments and feedback have been integrated into this essential resource. This edition has been compiled in machine-readable form and will be available online.

Physical Review

Physical Review
Author:
Publisher:
Total Pages: 1196
Release: 1998-06
Genre: Fluids
ISBN:
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Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.

Quantum Mechanics

Quantum Mechanics
Author: L D Landau
Publisher: Elsevier
Total Pages: 694
Release: 1981-12-18
Genre: Science
ISBN: 0080503489
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This edition has been completely revised to include some 20% of new material. Important recent developments such as the theory of Regge poles are now included. Many problems with solutions have been added to those already contained in the book.

Introduction to the Graphical Theory of Angular Momentum

Introduction to the Graphical Theory of Angular Momentum
Author: Ewald Balcar
Publisher: Springer
Total Pages: 227
Release: 2009-09-18
Genre: Science
ISBN: 3642031188
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Application of quantum mechanics in physics and chemistry often entails manipulation and evaluation of sums and products of coupling coefficients for the theory of angular momentum. Challenges encountered in such work can be tamed by graphical techniques that provide both the insight and analytical power. The book is the first step-by-step exposition of a graphical method grounded in established work. Copious exercises recover standard results but demonstrate the power to go beyond.

Quasi-Hopf Algebras

Quasi-Hopf Algebras
Author: Daniel Bulacu
Publisher: Cambridge University Press
Total Pages: 546
Release: 2019-02-21
Genre: Mathematics
ISBN: 1108632653
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This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras. Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete proofs. Many of the proofs are based on general categorical results; the same approach can then be used in the study of other Hopf-type algebras, for example Turaev or Zunino Hopf algebras, Hom-Hopf algebras, Hopfish algebras, and in general any algebra for which the category of representations is monoidal. Newcomers to the subject will appreciate the detailed introduction to (braided) monoidal categories, (co)algebras and the other tools they will need in this area. More advanced readers will benefit from having recent research gathered in one place, with open questions to inspire their own research.

Local Density Theory of Polarizability

Local Density Theory of Polarizability
Author: Gerald D. Mahan
Publisher: Springer Science & Business Media
Total Pages: 260
Release: 2013-06-29
Genre: Science
ISBN: 1489924868
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During the past decade the theoretical physics community has learned how to evaluate accurately polarizabilities and susceptibilities for many-electron systems such as atoms, solids, and liquids. The most accurate numerical technique employs a method often called the Time-Dependent Local Density Approximation, which is abbreviated TDLDA. The present volume is a review of recent research on the theory of po larizabilities and susceptibilities. Both authors have been doing these cal culations. However, this review surveys the entire field, summarizing the research of many contributors. The application of an external field, either ac or de, will induce a dipole moment which can be calculated and compared with experiment. For mod erately strong fields, both linear and nonlinear processes contribute to the moment. We cover topics such as polarizability, hyperpolarizability, pho toionization, phonons, and piezoelectricity. Density functional theory in the Local Density Approximation (LDA) has been shown to be a very accurate method for calculating ground state prop erties of electronic system. For static external fields, the induced moments are properties of the ground state. Then the calculation of the polarizability · is very accurate. For ac fields, the moment is not part of the ground state. However, the TDLDA methods are still very accurate.

John David Jackson

John David Jackson
Author: John David Jackson
Publisher: John Wiley & Sons
Total Pages: 421
Release: 2023-08-31
Genre: Science
ISBN: 1119880416
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A Course in Quantum Mechanics Unique graduate-level textbook on quantum mechanics by John David Jackson, author of the renowned Classical Electrodynamics A Course in Quantum Mechanics is drawn directly from J. D. Jackson’s detailed lecture notes and problem sets. It is edited by his colleague and former student Robert N. Cahn, who has taken care to preserve Jackson’s unique style. The textbook is notable for its original problems focused on real applications, with many addressing published data in accompanying tables and figures. Solutions are provided for problems that are critical for understanding the material and that lead to the most important physical consequences. Overall, the text is comprehensive and comprehensible; derivations and calculations come with clearly explained steps. More than 120 figures illustrate underlying principles, experimental apparatus, and data. In A Course in Quantum Mechanics readers will find detailed treatments of: Wave mechanics of de Broglie and Schrödinger, the Klein-Gordon equation and its non-relativistic approximation, free particle probability current, expectation values. Schrödinger equation in momentum space, spread in time of a free-particle wave packet, density matrix, Sturm-Liouville eigenvalue problem. WKB formula for bound states, example of WKB with a power law potential, normalization of WKB bound state wave functions, barrier penetration with WKB. Rotations and angular momentum, representations, Wigner d-functions, addition of angular momenta, the Wigner-Eckart theorem. Time-independent perturbation theory, Stark, Zeeman, Paschen-Back effects, time-dependent perturbation theory, Fermi’s Golden Rule. Atomic structure, helium, multiplet structure, Russell-Saunders coupling, spin-orbit interaction, Thomas-Fermi model, Hartree-Fock approximation. Scattering amplitude, Born approximation, allowing internal structure, inelastic scattering, optical theorem, validity criterion for the Born approximation, partial wave analysis, eikonal approximation, resonance. Semi-classical and quantum electromagnetism, Aharonov-Bohm effect, Lagrangian and Hamiltonian formulations, gauge invariance, quantization of the electromagnetic field, coherent states. Emission and absorption of radiation, dipole transitions, selection rules, Weisskopf-Wigner treatment of line breadth and level shift, Lamb shift. Relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, two-component reduction, hole theory, Foldy-Wouthuysen transformation, Lorentz covariance, discrete symmetries, non-relativistic and relativistic Compton scattering.