Angular Momentum in Quantum Mechanics

Angular Momentum in Quantum Mechanics
Author: A. R. Edmonds
Publisher: Princeton University Press
Total Pages: 155
Release: 2016-08-10
Genre: Science
ISBN: 1400884187

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.

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

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.

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

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.

Optically Polarized Atoms

Optically Polarized Atoms
Author: Marcis Auzinsh
Publisher: OUP Oxford
Total Pages: 400
Release: 2010-07-22
Genre: Science
ISBN: 0191576549

This book is addressed to upper-level undergraduate and graduate students involved in research in atomic, molecular, and optical physics. It will also be useful to researchers practising in this field. It gives an intuitive, yet sufficiently detailed and rigorous introduction to light-atom interactions with a particular emphasis on the symmetry aspects of the interaction, especially those associated with the angular momentum of atoms and light. The book will enable readers to carry out practical calculations on their own, and is richly illustrated with examples drawn from current research topics, such as resonant nonlinear magneto-opticals. The book comes with a software package for a variety of atomic-physics calculations and further interactive examples that is freely downloadable from the book's web page, as well as additional materials (such as power-point presentations) available to instructors who adopt the text for their courses.

Interpreting the Symbols and Types

Interpreting the Symbols and Types
Author: Kevin J. Conner
Publisher: Rich Brott
Total Pages: 220
Release: 1992
Genre: Religion
ISBN: 9780914936510

This book by Kevin Conner undertakes to interpret signs, symbols, and types that he discovers beneath the surface in biblical text.

Quantum Invariants of Knots and 3-Manifolds

Quantum Invariants of Knots and 3-Manifolds
Author: Vladimir G. Turaev
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 608
Release: 2016-07-11
Genre: Mathematics
ISBN: 3110435225

Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories

Handbook of Mathematical Functions

Handbook of Mathematical Functions
Author: Milton Abramowitz
Publisher: Courier Corporation
Total Pages: 1068
Release: 1965-01-01
Genre: Mathematics
ISBN: 9780486612720

An extensive summary of mathematical functions that occur in physical and engineering problems

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

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.

Atmospheric Evolution on Inhabited and Lifeless Worlds

Atmospheric Evolution on Inhabited and Lifeless Worlds
Author: David C. Catling
Publisher: Cambridge University Press
Total Pages: 595
Release: 2017-04-13
Genre: Science
ISBN: 0521844126

A comprehensive and authoritative text on the formation and evolution of planetary atmospheres, for graduate-level students and researchers.