Undergraduate Texts in Contemporary Physics

Primer for Point and Space Groups

Authors: Liboff, Richard

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About this Textbook

This text stems from a course I have taught a number of times, attended by students of material science, electrical engineering, physics, chemistry, physical chemistry and applied mathematics. It is intended as an intro­ ductory discourse to give the reader a first encounter with group theory. The work concentrates on point and space groups as these groups have the principal application in technology. Here is an outline of the salient features of the chapters. In Chapter 1, basic notions and definitions are introduced including that of Abelian groups, cyclic groups, Sylow's theorems, Lagrange's subgroup theorem and the rearrangement theorem. In Chapter 2, the concepts of classes and direct products are discussed. Applications of point groups to the Platonic solids and non-regular dual polyhedra are described. In Chapter 3, matrix representation of operators are introduced leading to the notion of irreducible representations ('irreps'). The Great Orthogonal­ ity Theorem (GOT) is also introduced, followed by six important rules relating to dimensions of irreps. Schur's lemma and character tables are described. Applications to quantum mechanics are discussed in Chapter 4 including descriptions of the rotation groups in two and three dimensions, the symmetric group, Cayley's theorem and Young diagrams. The relation of degeneracy of a quantum state of a system to dimensions of irreps of the group of symmetries of the system are discussed, as well as the basis properties of related eigenfunctions.

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 theory in nuclear and particle physics and other specific applications." (Zentralblatt für 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)


Table of contents (7 chapters)

  • Groups and Subgroups

    Liboff, Richard L.

    Pages 1-17

  • Classes and Platonic Solids

    Liboff, Richard L.

    Pages 18-35

  • Matrices, Irreps and the Great Orthogonality Theorem

    Liboff, Richard L.

    Pages 36-53

  • Quantum Mechanics, the Full Rotation Group, and Young Diagrams

    Liboff, Richard L.

    Pages 54-88

  • Space Groups, Brillouin Zone and the Group of k

    Liboff, Richard L.

    Pages 89-135

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-1-4684-9383-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-0-387-40248-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.95
price for USA
  • ISBN 978-1-4419-2317-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Primer for Point and Space Groups
Authors
Series Title
Undergraduate Texts in Contemporary Physics
Copyright
2004
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4684-9383-2
DOI
10.1007/978-1-4684-9383-2
Hardcover ISBN
978-0-387-40248-2
Softcover ISBN
978-1-4419-2317-2
Edition Number
1
Number of Pages
XIV, 220
Topics