Hoboken : : Wiley, , 2008.

1 online resource (478 p.)

Description based upon print version of record.. - ANGULAR MOMENTUM An Illustrated Guide to Rotational Symmetries for Physical Systems; CONTENTS; Preface; The Computer Interface; 1 Symmetry in Physical Systems; 1.1 Symmetries and invariances; 1.1.1 Symmetries and conservation laws; 1.1.2 Noether's theorem and Curie's principle; 1.2 Spatial symmetries; 1.2.1 Reflection symmetry in nature; 1.2.2 Translation symmetries; mosaics and crystals; 1.3 Rotational symmetries; 1.3.1 Active and passive rotations; Euler angles; 1.3.2 Coordinate systems for rotations; 1.3.3 Angular momentum and rotations: A cameo portrait. - 1.4 Discrete symmetries and quantum systems1.4.1 Parity symmetry; 1.4.2 Charge conjugation and time reversal; 1.4.3 Maxwell's equations and PCT; 1.4.4 PCT and the Pauli principle: Luder's theorem; 1.5 Broken symmetries from cosmetology to cosmology; Problems on symmetry in physical systems; 2 Mathematical and Quantal Preliminaries; 2.1 Matrix definitions and manipulations; 2.1.1 Linear spaces and operator matrix elements; 2.1.2 Inner and direct products of matrices; 2.1.3 Operations on matrices, and special properties; 2.1.4 Phase manipulation rules; 2.2 Transformations and operators. - 2.2.1 Similarity and symmetry transformations2.2.2 Unitarity: its interpretation in quantum mechanics; 2.2.3 Operator exponentials and commutators; 2.2.4 Raising and lowering operators; 2.3 Eigenvalues and eigenstates; 2.3.1 Eigenvalues of operators and matrices; 2.3.2 Diagonalizing matrices; 2.3.3 Eigenvectors as basis states; 2.4 Spinors and their properties; 2.4. 1 Definitions of spinors; 2.4.2 Representing spinors; rotations; 2.4.3 Objects that distinguish turns though 2π and 4π; 2.5 A primer on groups; 2.5.1 Group examples and definitions; 2.5.2 Group theory terminology. - 2.5.3 Representations of groups2.5.4 Interesting groups and their uses; 2.5.5 Irreducibility of a representation; 2.6 Mathematics, groups, and the physical sciences; Problems on mathematical and quantal preliminaries; 3 Rotational Invariance and Angular Momentum; 3.1 Infinitesimal rotations; the J operators; 3.1.1 Schemes for describing rotations; 3.1.2 Commutation relations of J operators; 3.1.3 The spherical-basis operators J + I , Jo, J-1; 3.2 Orbital angular momentum operators; 3.2.1 Infinitesimal rotations applied to spatial functions. - 3.2.2 Components of L in spherical polar coordinates3.2.3 The special role of the operator Lz; 3.3 Other representations of J operators; 3.3.1 The 2 x 2 matrix representation: Pauli matrices; 3.3.2 Eigenvectors of the Pauli matrices; 3.3.3 Finite rotations and Pauli matrices; 3.3.4 Spinor space and its operators; 3.4 Angular momentum eigenvalues and matrix elements; 3.4.1 Eigenvalues of J2 and Jz; irreducibility; 3.4.2 Matrix elements in the spherical basis; 3.4.3 Matrix elements in the Cartesian basis; 3.4.4 Operator matrices for j = 1/2, 1, and 3/2. - 3.4.5 Angular momentum: geometrical and dynamical. - Develops angular momentum theory in a pedagogically consistent way, starting from the geometrical concept of rotational invariance. Uses modern notation and terminology in an algebraic approach to derivations. Each chapter includes examples of applications of angular momentum theory to subjects of current interest and to demonstrate the connections between various scientific fields which are provided through rotations. Includes Mathematica and C language programs.

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