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And Its Application to the Quantum Mechanics of Atomic Spectra
1st Edition - January 1, 1959
Author: Eugene P. Wigner
Editor: H. S. W. Massey
9 7 8 - 1 - 4 8 3 2 - 7 5 7 6 - 5
Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with… Read more
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Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with particular reference to atomic spectra. The manuscript first takes a look at vectors and matrices, generalizations, and principal axis transformation. Topics include principal axis transformation for unitary and Hermitian matrices; unitary matrices and the scalar product; linear independence of vectors; and real orthogonal and symmetric matrices. The publication also ponders on the elements of quantum mechanics, perturbation theory, and transformation theory and the bases for the statistical interpretation of quantum mechanics. The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of atomic spectra. Discussions focus on eigenvalues and quantum numbers, spherical harmonics, and representations of the unitary group. The manuscript is a valuable reference for readers interested in the applications of group theoretical methods.
ContentsAuthor's Preface Translator's Preface 1. Vectors and Matrices Linear Transformations Linear Independence of Vectors 2. Generalizations 3. The Principal Axis Transformation Unitary Matrices and the Scalar Product The Principal Axis Transformation for Unitary and Hermitian Matrices Real Orthogonal and Symmetric Matrices 4. The Elements of Quantum Mechanics 5. Perturbation Theory 6. Transformation Theory and the Bases for the Statistical Interpretation of Quantum Mechanics 7. Abstract Group Theory Theorems for Finite Groups Examples of Groups Conjugate Elements and Classes 8. Invariant Subgroups The Factor Group Isomorphism and Homomorphism 9. The General Theory of Representations10. Continuous Groups11. Representations and Eigenfunctions 12. The Algebra of Representation Theory 13. The Symmetric Group Appendix to Chapter 13. A Lemma related to the Symmetric Group 14. The Rotation Groups 15. The Three-Dimensional Pure Rotation Group Spherical Harmonics The Homomorphism of the Two-Dimensional Unitary Group onto the Rotation Group The Representations of the Unitary Group The Representations of the Three-Dimensional Pure Rotation Group 16. The Representations of the Direct Product 17. The Characteristics of Atomic Spectra Eigenvalues and Quantum Numbers The Vector Addition Model Appendix t o Chapter 17. A Relationship Among Binomial Coefficients 18. Selection Rules and the Splitting of Spectral Lines 19. Partial Determination of Eigenfunctions from Their Transformation Properties 20. Electron Spin The Physical Basis for the Pauli Theory Invariance of the Description under Spatial Rotation Connection with Representation Theory Appendix to Chapter 20. Linearity and unitary Rotation Operators21. The Total Angular Momentum Quantum Number 22. The Fine Structure of Spectral Lines 23. Selection and Intensity Rules with Spin The Hönl-Kronig Intensity Formulas The Landé G-Formula The Interval Rule 24. Racah Coefficients Conjugate Complex Representations Symmetric Form of the Vector Coupling Coefficients Covariant and Contravariant Vector Coupling Coefficients Racah Coefficients Matrix Elements of Spin-Free Tensor Operators General Two-Sided Tensor Operators 25. The Building-Up Principle 26. Time Inversion Time Inversion and Antiunitary Operators Determination of the Time Inversion Operator Transformation of the Eigenfunctions under Antiunitary Operators Reduction of Corepresentations Determination of the Irreducible Corepresentations Consequences of Invariance under Time Inversion 27. Physical Interpretation and Classical Limits of Representation Coefficients, Three- and Six-j Symbols Representation Coefficients Vector Coupling Coefficients Racah Coefficients Appendix A. Conventions Appendix B. Summary of FormulasSubject Index