Group Theory : And Its Application to the Quantum Mechanics of Atomic Spectra

Group Theory: And Its Application To The Quantum Mechanics Of Atomic Spectra aims to describe the application of group theoretical methods to problems of quantum mechanics with specific reference to atomic spectra. Chapters 1 to 3 discuss the elements of linear vector theory, while Chapters 4 to 6 deal more specifically with the rudiments of quantum mechanics itself. Chapters 7 to 16 discuss the abstract group theory, invariant subgroups, and the general theory of representations. These chapters are mathematical, although much of the material covered should be familiar from an elementary course in quantum theory. Chapters 17 to 23 are specifically concerned with atomic spectra, as is Chapter 25. The remaining chapters discuss topics such as the recoupling (Racah) coefficients, the time inversion operation, and the classical interpretations of the coefficients. The text is recommended for physicists and mathematicians who are interested in the application of group theory to quantum mechanics. Those who are only interested in mathematics can choose to focus on the parts more devoted to that particular area of the subject. Content: Inside Front Cover Page ii Front Matter Page iii Copyright page Page iv Author's Preface Pages v-vi E.P. WIGNER Translator's Preface Page vii J.J. GRIFFIN 1 - Vectors and Matrices Pages 1-12 2 - Generalizations Pages 13-19 3 - The Principal Axis Transformation Pages 20-30 4 - The Elements of Quantum Mechanics Pages 31-39 5 - Perturbation Theory Pages 40-46 6 - Transformation Theory and the Bases for the Statistical Interpretation of Quantum Mechanics Pages 47-57 7 - Abstract Group Theory Pages 58-66 8 - Invariant Subgroups Pages 67-71 9 - The General Theory of Representations Pages 72-87 10 - Continuous Groups Pages 88-101 11 - Representations and Eigenfunctions Pages 102-111 12 - The Algebra of Representation Theory Pages 112-123 13 - The Symmetric Group Pages 124-141 14 - The Rotation Groups Pages 142-152 15 - The Three-Dimensional Pure Rotation Group Pages 153-170 16 - The Representations of the Direct Product Pages 171-176 17 - The Characteristics of Atomic Spectra Pages 177-194 18 - Selection Rules and the Splitting of Spectral Lines Pages 195-209 19 - Partial Determination of Eigenfunctions from their Transformation Properties Pages 210-219 20 - Electron Spin Pages 220-236 21 - The Total Angular Momentum Quantum Number Pages 237-250 22 - The Fine Structure of Spectral Lines Pages 251-265 23 - Selection and Intensity Rules with Spin Pages 266-283 24 - Racah Coefficients Pages 284-308 25 - The Building-Up Principle Pages 309-324 26 - Time Inversion Pages 325-348 27 - Physical Interpretation and Classical Limits of Representation Coefficients, Three- and Six- j Symbols Pages 349-356 Appendix A - Conventions Pages 357-360 Appendix B - Summary of Formulas Pages 361-364 Subject Index Pages 365-372 Pure and Applied Physics: A Series of Monographs and Textbooks Pages 373-374