Quantum theory of angular momentum : : Irreducible tensors, spherical harmonics, vector coupling coefficients 3 nj symbols / / by D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii.

• Author: Varshalovich, D. A.
• TeilnehmendeR: Moskalev, A. N.; Khersonskiĭ, V. K.
• Place / Publishing House: Singapore ;, Philadelphia : : World Scientific Pub.,, 1989.
• Year of Publication: 1989
• Language: English
• Physical Description: 1 online resource (528 p.)
• Notes: Translation of: Kvantovaia teoriia uglovogo momenta.

This is the most complete handbook on the quantum theory of angular momentum. Containing basic definitions and theorems as well as relations, tables of formula and numerical tables which are essential for applications to many physical problems, the book is useful for specialists in nuclear and particle physics, atomic and molecular spectroscopy, plasma physics, collision and reaction theory, quantum chemistry, etc. The authors take pains to write many formulae in different coordinate systems thus providing users with added ease in consulting this book. Each chapter opens with a comprehensive l

Table of Contents

CONTENTS; PREFACE; INTRODUCTION: BASIC CONCEPTS; Chapter 1 ELEMENTS OF VECTOR AND TENSOR THEORY; 1.1. COORDINATE SYSTEMS. BASIS VECTORS; 1.1.1. Cartesian Coordinate System; 1.1.2. Polar Coordinate System; 1,1.3. Spherical Coordinate System; 1.1.4, Helicity Basis Vector; 1.1.5. Relations Between Different Basis Vectors; 1.2. VECTORS. TENSORS; 1.2.1. Vector Components; 1.2.2. Scalar Product of Vectors; 1.2.3. Vector Product of Vectors; 1.2.4. Products Involving Three or More Vectors; 1.2.5. Tensors δik and εikl; 1.3. DIFFERENTIAL OPERATIONS; 1.3.1. Operator V; 1.3.2. Laplace Operator

1.3.3. Differential Operations on Scalars and Vectors1.4. ROTATIONS OF COORDINATE SYSTEM; 1.4.1. Description of Rotations in Terms of the Euler Angles; 1.4.2. Description of Rotations in Terms of Rotation Axis and Rotation Angle; 1.4.3. Description of Rotations in Terms of Unitary 2x2 Matrices. Cayley-Klein Parameters.; 1.4.4. Relations Between Different Descriptions of Rotations; 1.4.5. Rotation Operator; 1.4.6. Transformation of Cartesian Vectors and Tensors Under Rotations of Coordinate Systems. Rotation Matrix a; 1.4.7. Addition of Rotations; Chapter 2 ANGULAR MOMENTUM OPERATORS

2.1. TOTAL ANGULAR MOMENTUM OPERATOR2.1.1. Definition; 2.1.2. Commutation Relations; 2.1.3. Coordinate Inversion. Time Reversal; 2.1.4. Total Angular Momentum of a System. Orbital and Spin Angular Momenta; 2.2. ORBITAL ANGULAR MOMENTUM OPERATOR; 2.2.1. Definition; 2.2.2. Commutation Relations; 2.2.3. Explicit Form; 2.3. SPIN ANGULAR MOMENTUM OPERATOR; 2.3.1. Definition; 2.3.2. Commutation Relations; 2.3.3. Explicit Form; 2.3.4. Traces of Products of Spin Matrices; 2.4. POLARIZATION OPERATORS; 2.4.1. Definition; 2.4.2. Explicit Form

2.4.3. Properties of LM(S) under Transformations of the Coordinate System2.4.5. Commutators and Anticommutators; 2.4.6. Traces of Products of Polarization Operators; 2.5. SPIN MATRICES FOR 5 = 1/2; 2.5.1. Explicit Form; 2.5.2. Commutators and Anticommutators; 2.5.3. Products of Spin Matrices; 2.5.4. Functions of Spin Matrices; 2.5.5. Rotation Operators; 2.5.6. Traces of Products of Spin Matrices (S = 1/2); 2.6. SPIN MATRICES AND POLARIZATION OPERATORS FOR S = 1; 2.6.1. Spin S = 1; 2.6.2. Explicit Form; 2.6.3. Products of Spin and Polarization Matrices; 2.6.4. Functions of Spin Matrices

2.6.5. Operators of Coordinate Rotations2.6.6. Traces of Products of Spin Matrices; Chapter 3 IRREDUCIBLE TENSORS; 3.1. DEFINITION AND PROPERTIES OF IRREDUCIBLE TENSORS; 3.1.1. Definition; 3.1.2. Covariant and Contravariant Components; 3.1.3. Transformation of Irreducible Tensors Under a Rotation of the Coordinate System; 3.1.4. Transformation of Irreducible Tensors Under Inversion of the Coordinate System; 3.1.5. Double Tensors; 3.1.6. Examples of Irreducible Tensors; 3.1.7. Direct and Irreducible Tensor Products. Commutators of Tensor Products; 3.1.8. Scalar Products of Irreducible Tensors

3.2. RELATION BETWEEN THE IRREDUCIBLE TENSOR ALGEBRA AND VECTOR AND TENSOR THEORY