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Symmetries in quantum physics /
This text focuses on the physics of symmetries, developing symmetries and transformations through concrete physical examples and contexts rather than presenting the information axiomatically, mathematically, and abstractly. Readers are introduced gradually to advanced mathematical procedures, includ...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego :
Academic Press,
©1996.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction: Symmetry and the Selection of Variables. Algebraic Elements. Reduction Procedure and Irreducible Tensorial Sets. Further Aspects of Reduction. Structure of the Book. Quaternions. Part A: State Representatives and r<$>-Transformations: Their Construction and Properties. Infinitesimal Rotations and Angular Momentum:<$> 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<$> Coefficients. Part B: Tensorial Aspects of Quantum Physics.<$> 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<$> Coefficients:<$> Transformation Matrices and Their Analysis. Symmetrized Recoupling: 6-j<$> and9-j<$> Coefficients. Products of Operators. Combining Operators of Different Systems. Illustrations. Partially Filled Shells of Atoms or Nuclei:<$> Qualitative Discussion. Shell-wide Treatment. Algebra of Triple Tensors and Its Applications. PartC: Symmetries of Higher Dimensions.<$> 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.