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

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Elsevier, 2 déc. 2012 - 386 pages
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.
 

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Avis d'utilisateur  - agricolaoval - LibraryThing

A classic that I enjoyed immensely at the uni. Wigner has the rare gift of crystal clarity combined with the concern for his students. For most students group theory obviously is a mere tool, but this book made it a joy to study it for its own sake. Not recommended for holiday trips though. Consulter l'avis complet

Table des matières

Chapter 1 Vectors and Matrices
1
Chapter 2 Generalizations
13
Chapter 3 The Principal Axis Transformation
20
Chapter 4 The Elements of Quantum Mechanics
31
Chapter 5 Perturbation Theory
40
Chapter 6 Transformation Theory and the Bases for the Statistical Interpretation of Quantum Mechanics
47
Chapter 7 Abstract Group Theory
58
Chapter 8 Invariant Subgroups
67
Chapter 17 The Characteristics of Atomic Spectra
177
Chapter 18 Selection Rules and the Splitting of Spectral Lines
195
Chapter 19 Partial Determination of Eigenfunctions from Their Transformation Properties
210
Chapter 20 Electron Spin
220
Chapter 21 The Total Angular Momentum Quantum Number
237
Chapter 22 The Fine Structure of Spectral Lines
251
Chapter 23 Selection and Intensity Rules with Spin
266
Chapter 24 Racah Coefficients
284

Chapter 9 The General Theory of Representations
72
Chapter 10 Continuous Groups
88
Chapter 11 Representations and Eigenfunctions
102
Chapter 12 The Algebra of Representation Theory
112
Chapter 13 The Symmetric Group
124
Chapter 14 The Rotation Groups
142
Chapter 15 The ThreeDimensional Pure Rotation Group
153
Chapter 16 The Representations of the Direct Product
171
Chapter 25 The BuildingUp Principle
309
Chapter 26 Time Inversion
325
Chapter 27 Physical Interpretation and Classical Limits of Representation Coefficients Three and Sixj Symbols
349
Appendix A Conventions
357
Appendix B Summary of Formulas
361
Subject Index
365
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