Group Theory in Chemistry and Spectroscopy


Book Description

This handbook on group theory is geared toward chemists and experimental physicists who use spectroscopy and require knowledge of the electronic structures of the materials they investigate. Accessible to undergraduate students, it takes an elementary approach to many of the key concepts. Rather than the deductive method common to books on mathematics and theoretical physics, the present volume introduces fundamental concepts with simple examples, relating them to specific chemical and physical problems. The text is centered on detailed analysis of examples. Since neither chemists nor spectroscopists require theorem proofs, very few appear here. Instead, the focus remains on the principal conclusions, their meaning, and their use. In keeping with the text's practical bias, the main results of group theory are presented in all sections as procedures, making possible their systematic and step-by-step-application. Each chapter contains problems that develop practical skill and provide a valuable supplement to the text.




Group Theory


Book Description

Group Theory and its Application to the Quantum Mechanics of Atomic Spectra describes the applications of group theoretical methods to problems of quantum mechanics with particular reference to atomic spectra. The manuscript first takes a look at vectors and matrices, generalizations, and principal axis transformation. Topics include principal axis transformation for unitary and Hermitian matrices; unitary matrices and the scalar product; linear independence of vectors; and real orthogonal and symmetric matrices. The publication also ponders on the elements of quantum mechanics, perturbation theory, and transformation theory and the bases for the statistical interpretation of quantum mechanics. The book discusses abstract group theory and invariant subgroups, including theorems of finite groups, factor group, and isomorphism and homomorphism. The text also reviews the algebra of representation theory, rotation groups, three-dimensional pure rotation group, and characteristics of atomic spectra. Discussions focus on eigenvalues and quantum numbers, spherical harmonics, and representations of the unitary group. The manuscript is a valuable reference for readers interested in the applications of group theoretical methods.













Group Theory and Its Applications


Book Description

Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with the representation and tensor operators of the unitary groups. The next chapter describes wave equations, both Schrödinger’s and Dirac’s for a wide variety of potentials. These topics are followed by discussions of the applications of dynamical groups in dealing with bound-state problems of atomic and molecular physics. A chapter explores the connection between the physical constants of motion and the unitary group of the Hamiltonian, the symmetry adaptation with respect to arbitrary finite groups, and the Dixon method for computing irreducible characters without the occurrence of numerical errors. The last chapter deals with the study of the extension, representation, and applications of Galilei group. This book will prove useful to mathematicians, practicing engineers, and physicists.




Selected Papers of Léon Rosenfeld


Book Description

The decision to undertake this volume was made in 1971 at Lake Como during the Varenna summer school ofthe Italian Physical Society, where Professor Leon Rosenfeld was lecturing on the history of quantum theory. We had long been struck by the unique blend of epistemological, histori cal and social concerns in his work on the foundations and development of physics, and decided to approach him there with the idea of publishing a collection of his papers. He responded enthusiastically, and agreed to help us select the papers; furthermore, he also agreed to write a lengthy introduction and to comment separately on those papers that he felt needed critical re-evaluation in the light of his current views. For he was still vigorously engaged in both theoretical investigations of, and critical not reflections on the foundations of theoretical physics. We certainly did conceive of the volume as a memorial to a 'living saint', but rather more practically, as a useful tool to place in the hands of fellow workers and students engaged in wrestling with these difficult problems. All too sadly, fate has added a memorial aspect to our labors. We agreed that in order to make this book most useful for the con temporary community of physicists and philosophers, we should trans late all non-English items into English.




NBS Special Publication


Book Description