Keywords:
Quantum theory.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (431 pages)
Edition:
1st ed.
ISBN:
9781483149387
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=1834307
Language:
English
Note:
Front Cover -- Applied Group Theory -- Copyright Page -- Table of Contents -- Preface -- PART I -- Chapter 1. Symmetry -- 1.1. Symmetry Operations -- 1.2. Definition of a Group -- 1.3. Symmetry in Nature -- Chapter 2. Theory of Groups -- 2.1. Further Definitions -- 2.2. Subgroups -- 2.3. Classes -- 2.4. Matrices -- 2.5. Matrices and the Symmetry Operations of the Square -- 2.6. Matrix Representations of a Group -- 2.7. Irreducible (Matrix) Representations of a Group -- 2.8. The Deduction of the Irreducible Representations of a Group -- 2.9. The Direct Product of Two Groups -- 2.10. Group Theory and Quantum Mechanics, Wigner's Theorem -- Chapter 3. Crystallographic Groups -- 3.1. Point Groups -- 3.2. The Derivation of the Point Groups and their Character Tables -- 3.3. The Basis of a Representation -- 3.4. Bravais Lattices -- 3.5. Space Groups -- 3.6. Seitz Space-group Symbols -- Chapter 4. The Rotation, Symmetric and Lorentz Groups -- 4.1. The Rotation Group -- 4.2. The Representations of the Rotation Group -- 4.3. The Spherical Harmonics and the Rotation Group -- 4.4. The Permutation Group, or Symmetric Group, S(n) -- 4.5. Young's Tableaux -- 4.6. Special Relativity and the Lorentz Group -- Chapter 5. Vibrations in Molecules and Solids -- 5.1. Vibrations of Molecules, Normal Modes -- 5.2. Example, the Normal Modes of the Methane Molecule -- 5.3. Vibrations of Solids, Phonons -- 5.4. Brillouin Zone Theory -- 5.5. Infrared and Raman Activity of the Normal Modes -- Chapter 6. Electronic States in Atoms, Molecules and Solids -- 6.1. Wave Functions of Electrons in Atoms -- 6.2. Wave Functions of Electrons in Molecules -- 6.3. The Jahn-Teller Effect -- 6.4. The Splitting of Atomic Energy Levels in Crystals -- 6.5. Wave Functions of Electrons in Solids -- Chapter 7. Atoms, Nuclei and Elementary Particles.
,
7.1. The Principle of Antisymmetry and the Pauli Exclusion Principle -- 7.2. The Spherical Harmonics and Angular Momentum -- 7.3. Selection Rules for Electrons in Atoms -- 7.4. Spin, SU(2) -- 7.5. Nuclei, Isobaric Spin -- 7.6. "Elementary" Particles, SU(3), etc -- Chapter 8. Further Topics -- 8.1. Double Groups -- 8.2. Magnetic Point Groups and Magnetic Space Groups -- 8.3. Time Reversal and the Kramers Degeneracy -- 8.4. Symmetry Properties of Tensors -- 8.5. Waveguide Junctions -- 8.6. Campanological Groups -- GUIDED BIBLIOGRAPHY -- REFERENCES -- PART II -- Chapter 1. The Elastic Characteristic Vibrations of Symmetrical Systems -- Chapter 2. The Degeneracy, Selection Rules, and Other Properties of the Normal Vibrations of Certain Polyatomic Molecules -- Explanation of Tables -- Discussion of Results -- Molecules with Three Atoms -- Molecules with Four Atoms -- Molecules with Five Atoms -- Molecules with Six Atoms -- Molecules with Seven Atoms -- Molecules with Eight Atoms -- Molecules with Nine Atoms -- Chapter 3. Stability of Polyatomic Molecules in Degenerate Electronic States. I Orbital Degeneracy -- Introduction -- 1. Two Examples -- 2. General Theorem -- 3. Mathematical Formulation and Group-theoretical Considerations -- 4. Proof of General Theorem -- 5. Conclusion -- Summary -- References -- Chapter 4. Splitting of Terms in Crystals -- I. Solution by Theory of Groups -- II. The Eigenfunctions to Zero-order Approximation in the Crystal -- Chapter 5. On the Reduction of Space Groups -- Introduction -- 1. The Theory of Space Groups -- 2. A Theorem Concerning the Reduction of Finite Solvable Groups -- 3. Additional Simplifying Developments -- 4. Concerning Physical Applications -- Chapter 6. Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals -- I -- II -- III -- IV -- V -- VI. Body-centered Cubic Lattice.
,
VII. Face-centered Cubic Lattice -- Chapter 7. On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- Chapter 8. "Double" Crystallographic Groups -- Chapter 9. Magnetic Symmetry of Crystals -- 1. Introduction -- 2. Some Properties of the Transformations Introduced Above. Statement of the Problem -- 3. Algorithm for Constructing the Point Groups -- 4. List of Groups of Point Transformations for the Symmetry of Crystals with a Mean Current Density -- 5. Possible Applications of the Groups of Point Symmetry Transformations of Crystals -- APPENDIX -- The Character Tables of the Thirty-two Point Groups -- Hints to Solutions of the Exercises -- INDEX.
Permalink