Group Theory and Quantum Mechanics (Dover Books on Chemistry) by Michael Tinkham | (PDF) Free Download

Description

This graduate-level text develops the aspects of group theory most relevant to physics and chemistry (such as the theory of representations) and illustrates their applications to quantum mechanics. The first five chapters focus chiefly on the introduction of methods, illustrated by physical examples, and the final three chapters offer a systematic treatment of the quantum theory of atoms, molecules, and solids.The formal theory of finite groups and their representation is developed in Chapters 1 through 4 and illustrated by examples from the crystallographic point groups basic to solid-state and molecular theory. Chapter 5 is devoted to the theory of systems with full rotational symmetry, Chapter 6 to the systematic presentation of atomic structure, and Chapter 7 to molecular quantum mechanics. Chapter 8, which deals with solid-state physics, treats electronic energy band theory and magnetic crystal symmetry. A compact and worthwhile compilation of the scattered material on standard methods, this volume presumes a basic understanding of quantum theory.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have attempted to read other books on group theory, especially those intended for physicists, including Weyl’s book

⭐. Tinkham’s book, however, is the only one that I have been able to understand relatively well. Tinkham gently takes you by the hand and starts you out on a tutorial that addresses the symmetry of a simple example from plane geometry, and then gradually builds up to more sophisticated problems. Character tables and the various orthogonality and normalization relations that make them useful are developed and used for both simple (e.g. plane geometry) and more sophisticated problems. Lie Groups, Schur’s Lemma, angular momentum, crystal symmetry, and nature’s inability to conserve parity are among the topics addressed.The treatment of Lorentz and Poincare groups required for a more sophisticated understanding of quantum field theory, however, is not included in this book–for those topics Weinberg’s (

⭐) suggestion of Tung’s

⭐would seem to be reasonable. I was also not able to understand Tinkham’s proof of the Vector Addition Theorem for angular momentum. I found a version of the proof that I could understand, however, in Wigner’s book

⭐, and I display this proof along with my review of Wigner’s book.

⭐This book is great. It’s opened my eyes to the symmetries that can provide intuition for a lot of the results in quantum mechanics, molecular theory, and solid state physics. I’ve now become a lot more comfortable with how operators’ invariances give rise to their properties. Diagonalization is much more natural of an idea to me now.Prerequisites & Notes: Already be familiar with group theory and quantum mechanics (the latter at the undergraduate level is fine). The first three chapters present a dense overview of group theory and notation that will be used in the rest of the book. I’ve had two introductions to group theory and that was still barely enough to get me through those chapters. The content was nevertheless interesting, so long as you reread it enough to understand what Tinkham is going on about! (Again, pretty dense)

⭐Me agrada mucho para el estudio del acoplamiento espín-órbita.This book has the advantage of applying group theory directly to solvable physical problems. In most areas of applied physics it isvery important to know the basics concepts of group theory, butthere is no need to have a deep knowledge as well as to know how toproof all the main theorems. As an introductory course for undergradstudents this book is well recommended.

⭐Great for QM lovers!

⭐Great book great price

⭐My background is that of theoretically inclined inorganic chemist and this review is intended for those with interests in inorganic and physical chemistry or solid-state chemistry/physics.Tinkham’s text is the first textbook one should go to for a reasonably rigorous introduction to the theory and use of group representations in physics and theoretical chemistry. Modern theoretical chemists should become familiar with all of this book, with the possible exception of the some of the material in Chapter 5 that will be applicable only to physicists (and not a lot of that, actually). The pervasiveness of band theory, even in general inorganic chemistry journals now, should convince chemists who teach this subject to include a lot of Chapter 8 (Solid-State Theory) and chemical theorists will even have to go beyond the symmorphic groups treated here. The purely mathematical aspects of the subject are treated briefly, but much more completely, than “chemical group theory books” like Cotton’s, for example. Naturally, this comes at a price of more mathematical abstractness, but that is unavoidable. These sections, like the rest of the book, are very well written. Chapter 7, on applications to molecular quantum mechanics, is now quite dated. It was quite incomplete even when written, since it did not include any discussion of ligand-field theory. The effects of antisymmetric wavefunctions for electrons are touched on briefly in Chapter 5 (atoms), but are not adequately accounted for in discussion of molecules. (Incidentally, the failure to use Mulliken notation in molecular QM is an unfortunate annoyance.) These objections aside, this book is an excellent buy for the price of a Dover edition. Indeed, if I’d included price in my rating, it would be 5 stars – easily!

⭐Even after taking 3 semesters of quantum mechanics, I felt like I had a pretty shaky grasp on topics such as selection rules and the addition of angular momenta. I had heard about the important role that group theory plays in quantum mechanics, so I took a mathematics class in abstract algebra. Though this covered a lot of interesting topics in group structure and ring theory, I was left with almost no idea how the material applied to quantum mechanics. Tinkham’s book is invaluable in that it develops the parts of group theory that are extremely relevant to physics and chemistry such as the theory of representations (topics that mathematicians seem bored by) and then shows beautifully how it applies to quantum mechanics. Not only did I understand the selection rules, angular momentum, etc… I had a much better understanding of quantum mechanics overall. Group theory makes much more evident what is meant by “good quantum numbers”, where degeneracies come from, and other basic issues in quantum mechanics. Particularly clever was the discussion of the Bloch wavefunction ansatz as a consequence of the Abelian symmetry group of a periodic crystal lattice. Invaluable for quantum chemistry, a subject which is touched on, but which was not nearly as developed when the book was written as it is today. Tinkham knows his math, but he knows his physics even better. If you have any interest in quantum mechanics, get this book!

⭐BVery good book to read for group theory

⭐The printing of the book is seriously disappointing. It seems just a horrible copy version. Very low quality! But the content is good.

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