Group Theory: And Its Application to the Quantum Mechanics of Atomic SpectraGroup 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. |
Contents
Vectors and Matrices | 1 |
Generalizations | 15 |
The Principal Axis Transformation for Unitary and Hermitian | 26 |
Copyright | |
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angle angular momentum antisymmetric antiunitary applies arbitrary assume atom calculation Chapter character coefficients commutes complex components configuration conjugate consider constant coordinate system corresponding coset denoted determined diagonal matrix direct product eigen eigenfunctions eigenvalue energy equal equivalent expression follows group elements Hence Hermitian identity implies integral invariant subgroup inversion irreducible representations isomorphic j₁ j₂ kth row levels linear combinations linearly independent magnetic field matrix elements multiplet system multiplication number of electrons obtained orbital quantum number orthogonal parameters particles permutation perturbation polarized pure rotation group quantum mechanics rotation group rows and columns scalar product Schrödinger equation sentation similarity transformation six-j symbols space spin coordinates substitution summation symmetric group tensor Theorem theory three-j symbols transition two-dimensional unitary group unitary matrix values vanish variables vector wave function Z-axis zero