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Preface to the Second Edition vii

1. Elements of Quantum Mechanics

1. Review of ClassicalMechanics

2. Vector Spaces and Linear Operators

3. Basic Postulates of Quantum Mechanics

4. Compatible Observables and Complete Set of Commuting Operators

5. Formof the Operators

6. Matrix Formalism and Transformation Theory

7. General Theory of Angular Momentum

8. Time-Independent Perturbation Theory

9. Time-Dependent Perturbation Theory

References

2. Elements of Group Theory

1. Properties of a Group

2. Classes

3. Theory of Representations

4. Schur's Lemma and Orthogonality Relations

5. Characters of a Group

6. Properties of the Irreducible Representations of a Group

7. The Direct Product Representation

8. Product Groups and Their Representations

9. Summary of Rules

10. Groups of Real Orthogonal Matrices

11. Space Groups and Symmetry of Crystalline Solids

12. The Irreducible Representations of a Group of Primitive Translations

13. The Irreducible Representations of Space Groups

References

3. Connection of Quantum Mechanics with Group Theory 115

1. The Effect of an Orthogonal Coordinate Transformation on the Vectors of a Hilbert Space

2. The Symmetry Group of the Schr¨odinger Equation

3. The Fundamental Theorem for Functions and OperatorsTransforming Irreducibly

4. The Construction of Functions Transforming Irreducibly

5. The Full Rotational Group and the Quantum Theory of Angular Momentum

6. The Spin of the Electron and the Double Valued Representations

7. The Kramers'Degeneracy

8. The Symmetric Group of the Hamiltonian and the Pauli Principle

References

4. The Hydrogen Atom 155

1. The Unperturbed Hamiltonian

2. The Spin-Orbit Interaction

3. The Zeeman Interaction

4. Group Theoretical Considerations for the H Atom

References

5. The Complex Atom: Multiplet Theory 165

1. The Helium Atom

2. The Many Electron Atom

3. Group Theoretical Considerations for a Complex Atom

4. The Energies of Spectral Terms

5. Hund's Rules and the Principle of Equivalence of Electrons and Holes

6. The Spin-Orbit Splitting of Terms

7. An Example of Spin-Orbit and Zeeman Splitting

References

……

6. The Magnetic Ion in a Crystal: The Role of Symmetry 216

7. The Weak Field Scheme

8. The Medium Field Scheme

9. The Strong Field Scheme

10. Covalent Bonding and Its Effect on MagneticIons in Crystals

11. The Quantum Theory of the Radiation Field

12. Molecular Vibrations

13. Lattice Vibrations

14. The Ion-Photon Interaction: Absorption and Emission of Radiation

15. The Judd-Ofelt Theory

16. The Ion-Vibration Interaction. Radiationless Processes， Thermal Shift， and Broadening of Sharp Lines

17. Vibrational-Electronic Interaction and Spectra

18. Energy Transfer Among Ions in Solids

19. Absorption Spectra of Magnetic Ions in Crystals

20. Fluorescence Spectra of Magnetic Ions in Crystals

21. Elements of Laser Theory

References

Subject Index

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