| Introduction: Symmetry and the Selection of Variables |
| Algebraic Elements |
| Reduction Procedure and Irreducible Tensorial Sets |
| Further Aspects of Reduction |
| Structure of the Book |
| Quaternions |
| State Representatives and r -Transformations: Their Construction and Properties / Part A： |
| Infinitesimal Rotations and Angular Momentum |
| Basic Relations |
| Analytical Example: Infinitesimal Transformation of Cartesian Coordinates |
| The Angular Momentum Matrices of Quantum Mechanics |
| The Fundamental Representation |
| Frame Reversal and Complex Conjugation |
| Analytical Representation and Implications of Frame Reversal |
| Contragradience and the Construction of Invariants |
| Cartesian Base for Integer j |
| [greater than or equal to sign here]1 |
| Standard r -Transformation Matrices and Their Applications |
| Explicit Form and Properties |
| Macroscopic Applications |
| Applications to Quantum Physics |
| Coordinate Inversion and Parity Eigenfunctions |
| Reduction of Direct Products (Addition of Angular Momenta) |
| Structure and Properties of the Reducing Matrix |
| Reduction of r -Transformation Products |
| Irreducible Product Sets |
| Symmetrization of Wigner Coefficients: Invariant Triple Product and 3-j |
| Coefficients |
| Tensorial Aspects of Quantum Physics / Part B： |
| Tensorial Sets of Quantum Operators |
| The Liouville Representation of Quantum Mechanics |
| Quantum Mechanics of Particles with Spin 1/2 |
| Two-Level Systems |
| Particles With Spin j >1/2: Wigner-Eckart Theorem |
| Systems with 2j +1 Levels |
| Transfer of Angular Momentum |
| Calculation of Matrix Elements |
| Recoupling Transformations: 6-j and 9-j |
| Transformation Matrices and Their Analysis |
| Symmetrized Recoupling: 6-j and9-j |
| Products of Operators |
| Combining Operators of Different Systems |
| Illustrations |
| Partially Filled Shells of Atoms or Nuclei |
| Qualitative Discussion |
| Shell-wide Treatment |
| Algebra of Triple Tensors and Its Applications |
| Symmetries of Higher Dimensions / Part C： |
| Discrete Transformations of Coordinates |
| Point Symmetry Operations and Their Groups |
| Characters of Group Representations and Their Applications |
| Symmetries of Molecules and Crystals |
| Rotation Groups in Higher Dimensions: Multiparticle Problems |
| Four-Dimensional Rotations: the Coulomb-Kepler Problem |
| Orthogonal Groups in Higher Dimensions |
| Further Developments |
| Lorentz Transformations and the Lorentz and Poincare Groups |
| Lorentz Transformations |
| Generators and Representations of the Lorentz Group |
| The Inhomogenous Lorentz (Poincare) Group |
| Field Representations |
| Symmetries of the Scattering Continuum |
| Symmetries of Radial Eigenfunctions |
| The Full Noninvariance Group of Hydrogen |
| Dynamics as Symmetry Transformations |
| Bibliography |
| Index |
| Introduction: Symmetry and the Selection of Variables |
| Algebraic Elements |
| Reduction Procedure and Irreducible Tensorial Sets |
図書
