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
Industry Reviews
From the reviews:
"I teach a course which involves symmetry and point groups so I was especially pleased to have been asked to do this review. ... The material is covered succinctly but in surprising depth for the size of the volume. ... The text is clear throughout and the nomenclature is consistent. ... It is more likely to provide a solid background for researchers and postgraduate students entering a new field or undergraduates dealing with advanced topics which are especially group theory intensive." (Contemporary Physics, Vol. 46 (4), July-August, 2005)
"This small volume may prove most useful to the lecturer in symmetry and/or group theory who will find many brief, interesting, and unusual ideas and approaches to many of different topics. ... The individual chapters are followed by interesting questions that are designed to extend the applications discussed in the chapter. ... Again these questions will surely prove useful to the lecturer for future lectures and exams!" (Gary J. Long, Fernande Grandjean, Physicalia, Vol. 57 (3), 2005)
"Liboff's book provides a general introduction to the subject with applications in quantum mechanics and solid state physics. ... A distinguishing feature of the book is the generous use of figures and illustrations ... . The book could be used in a short course on group theory or to supplement courses on quantum mechanics or solid state physics. It also provides a relatively painless introduction to the subject for those who need to learn it later in life." (Serdar Kuyucak, The Physicist, Vol. 41 (5), 2004)
"Written in the spirit of Liboff's text on quantum mechanics, the book is an introductory text for undergraduates in physics, engineering, materials science, and chemistry. With its selection and arrangement of examples, the book traces at every turn the physical implications of abstract concepts. It provides a solid background for those students who expect to use group theoryin nuclear and particle physics and other specific applications." (Zentralblatt fuer Didaktik der Mathematik, Mai, 2004)
"This text, a part of the series Undergraduate Texts in Contemporary Physics, is intended as an introductory book on group theory for undergraduates in materials science, electrical engineering, physics, chemistry, physical chemistry, and applied mathematics. ... Overall, this text will probably be useful as a reference to those in physics, materials science, and applied mathematics ... . The text would be ... useful for those involved in the advanced study of solid state materials, as this tends to be the focus of the work." (Christopher Stromberg, Theoretical Chemistry Accounts, Vol. 115 (1), 2006)
