Primer for Point and Space Groups
By: by Richard L. Liboff
Series: Undergraduate Texts in Contemporary Physics; Undergraduate texts in contemporary physics
Publisher: Springer New York
Published: 2004
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 220
ISBN-13: 9781441923172; 9781468493832
Subjects: Physical organic chemistry; Group theory; Computer engineering; Physics
Description: Written in the spirit of Liboff's acclaimed text on quantum mechanics, Primer for Point and Space Groups is an ideal introductory text for undergraduates in physics, engineering, materials science, chemistry. With its shrewd selection and arrangement of examples, the book traces at every turn the physical implications of abstract concepts. The book will therefore provide a solid background for those students who expect to use group theory in nuclear and particle physics and other specific applications. Among the many introductions to group theory currently available, few are as closely attuned to the needs of the applied scientist without compromise to the logic and lucidity of the presentation. Here are some of the applications covered in Liboff's Primer for Point and Space Groups: Applications to Quantum Mechanics: - Irreducible representations and degeneracy - Full rotation group; SU(2) group; angular momentum - Symmetry group and the wavefunction - Young diagrams and the wavefunction - Degenerate perturbation theory - Great Orthogonality Theorem Applications to Solid-State Physics: - Translation and Crystallographic Point Groups - Holohedral groups - Bloch waves and space groups - Bravais lattice - Energy -band eigenenergies - Seitz operator, (Translation and Rotation) - Glide-plane and screw operators - Diamond structure - Group of {bf k} and Star of $bf k $. - Space group of {bf k} - Time reversal and Space inversion effects on the - wavefunction and eigenenergies - Symmorphic group - Factor Group theorem Applications to Material Media: - Splitting of electron levels in crystals with symmetry - Correlation diagrams - Neumann's Principle - Polarizability - Piezoelectric effect - Classification of magnetic crystals - Black and white groups.
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Table of contents: title: Groups and Subgroups; title: Classes and Platonic Solids; title: Matrices, Irreps and the Great Orthogonality Theorem; title: Quantum Mechanics, The Full Rotation Group, and Young Diagrams; title: Space Groups, Brillouin Zone and Group of k; title: Atoms in Crystals and Correlation Diagrams; title: Elements of Abstract Algebra and the Galois Group.