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Cambridge University Press eBooks

Angular Momentum in Quantum Physics

Lawrence C. Biedenharn, James D. Louck, Peter Carruthers

Published Dec 28, 1984• 874 citations
Publisher

Abstract

This 1985 text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature and shows how this concept relates to applied areas of research in modern quantum physics.
DOI
10.1017/cbo9780511759888

Related papers

Angular Momentum in Quantum Physics: Theory and Application

Lawrence C. Biedenharn, James D. Louck

This 1985 text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature.

•Dec 28, 1984•483 citations

Angular Momentum

Arjun Berera, Luigi Del Debbio

Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.

Cambridge University Press eBooks•Oct 21, 2021•0 citations

Introduction

L. C. Biedenharn, J. D. Louck

It has been the purpose of the monograph Angular Momentum in Quantum Physics (AMQP) to develop comprehensively those aspects of angular momentum theory that are required in carrying out research in modern physics and chemistry. The emphasis there was principally on physical concepts and the symmetry principles that underlie the general applicability of angular momentum theory to a broad area of physical phenomena. Mathematical techniques were introduced within the context of the physical concepts themselves. Physical applications of angular momentum theory are to a large extent applications of specific properties of Wigner or Racah functions (more generally of 3 n-j coefficients) or of the representation functions themselves. Such applications tend to emphasize the “numerical” aspects of these functions and thus obscure the relationships to other areas of mathematics. The purpose of the present monograph is to show by specific examples the many interrelations that exist between concepts originating in angular momentum theory and various areas of mathematics. It turns out that this is a substantial task—the diversity of the interrelations is far greater than might be thought. Even a brief acquaintance with the contents of AMQP will show that the concept that recurs again and again in physical applications is that of an irreducible tensor operator with respect to a group [in our case, SU (2), the quantal rotation group]. Indeed, it is this concept that carries the mathematical apparatus of the physical theory beyond the related but much simpler results of the Lie algebraic theory of the angular momentum itself and the implied representation theory of the group SU (2).

Cambridge University Press eBooks•Dec 28, 1984•0 citations

Angular Momentum

D.M. Brink, G.R. Satchler

Abstract This book introduces the quantum theory of angular momentum to students who are unfamiliar with it and develops it to a stage useful for research. The first part contains the basic theory of rotations and angular momentum. As the book aims to emphasize applications, mathematical details are avoided and difficult theorems stated without proof. The second part contains examples of applications to a wide range of physical phenomena and presents a collection of results helpful in solving problems.

•Feb 10, 1994•111 citations

Theory of Angular Momentum I: Operators, Algebras, Representations

Horatiu Nastase

Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.

Cambridge University Press eBooks•Aug 4, 2022•0 citations

Quantum Mechanics I - PHYS507

Altuğ Özpineci

Fundamental concepts; quantum dynamics; theory of angular momentum and central potential problems; Wigner-Eckart theorem and addition of angular momenta; symmetry in quantum mechanics; approximation methods for time-independent and time-dependent perturbations.

•Jan 1, 2017•0 citations
Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.
It has been the purpose of the monograph Angular Momentum in Quantum Physics (AMQP) to develop comprehensively those aspects of angular momentum theory that are required in carrying out research in modern physics and chemistry. The emphasis there was principally on physical concepts and the symmetry principles that underlie the general applicability of angular momentum theory to a broad area of physical phenomena. Mathematical techniques were introduced within the context of the physical concepts themselves. Physical applications of angular momentum theory are to a large extent applications of specific properties of Wigner or Racah functions (more generally of 3 n-j coefficients) or of the representation functions themselves. Such applications tend to emphasize the “numerical” aspects of these functions and thus obscure the relationships to other areas of mathematics. The purpose of the present monograph is to show by specific examples the many interrelations that exist between concepts originating in angular momentum theory and various areas of mathematics. It turns out that this is a substantial task—the diversity of the interrelations is far greater than might be thought. Even a brief acquaintance with the contents of AMQP will show that the concept that recurs again and again in physical applications is that of an irreducible tensor operator with respect to a group [in our case, SU (2), the quantal rotation group]. Indeed, it is this concept that carries the mathematical apparatus of the physical theory beyond the related but much simpler results of the Lie algebraic theory of the angular momentum itself and the implied representation theory of the group SU (2).
Abstract This book introduces the quantum theory of angular momentum to students who are unfamiliar with it and develops it to a stage useful for research. The first part contains the basic theory of rotations and angular momentum. As the book aims to emphasize applications, mathematical details are avoided and difficult theorems stated without proof. The second part contains examples of applications to a wide range of physical phenomena and presents a collection of results helpful in solving problems.
Written for a two-semester graduate course in Quantum Mechanics, this comprehensive text helps develop the tools and formalism of Quantum Mechanics and its applications to physical systems. It suits students who have taken some introductory Quantum Mechanics and Modern Physics courses at undergraduate level, but it is self-contained and does not assume any specific background knowledge beyond appropriate fluency in mathematics. The text takes a modern logical approach rather than a historical one and it covers standard material, such as the hydrogen atom and the harmonic oscillator, the WKB approximations and Bohr-Sommerfeld quantization. Important modern topics and examples are also described, including Berry phase, quantum information, complexity and chaos, decoherence and thermalization, nonstandard statistics, as well as more advanced material such as path integrals, scattering theory, multiparticles and Fock space. Readers will gain a broad overview of Quantum Mechanics, as solid preparation for further study or research.