Search results for: the-theory-of-groups-and-quantum-mechanics

The Theory of Groups and Quantum Mechanics

Author : Hermann Weyl
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This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.

Group Theory and Quantum Mechanics

Author : Michael Tinkham
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Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.

Group Theory and Quantum Mechanics

Author : Bartel L. van der Waerden
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The German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.

Theory of Groups in Classical and Quantum Physics Mathematical structures and the foundations of quantum theory translated from the French by H Ingram

Author : Théo Kahan
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Theory of Groups in Classical and Quantum Physics Mathematical structures and the foundations of quantum theory translated by H Ingram

Author : Théo Kahan
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The Theory of Groups and Quantum Mechanics

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Group Theory

Author : Eugene Wigner
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Group Theory: And Its Application To The Quantum Mechanics Of Atomic Spectra aims to describe the application of group theoretical methods to problems of quantum mechanics with specific reference to atomic spectra. Chapters 1 to 3 discuss the elements of linear vector theory, while Chapters 4 to 6 deal more specifically with the rudiments of quantum mechanics itself. Chapters 7 to 16 discuss the abstract group theory, invariant subgroups, and the general theory of representations. These chapters are mathematical, although much of the material covered should be familiar from an elementary course in quantum theory. Chapters 17 to 23 are specifically concerned with atomic spectra, as is Chapter 25. The remaining chapters discuss topics such as the recoupling (Racah) coefficients, the time inversion operation, and the classical interpretations of the coefficients. The text is recommended for physicists and mathematicians who are interested in the application of group theory to quantum mechanics. Those who are only interested in mathematics can choose to focus on the parts more devoted to that particular area of the subject.

Applications of Group Theory in Quantum Mechanics

Author : M. I. Petrashen
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Geared toward theoretical physicists, this advanced text explores the value of modern group-theoretical methods in quantum theory. It explains the theory of groups and their matrix representations, developing them to the level required for applications. The main focus rests upon point and space groups, with applications to electronic and vibrational states. 1969 edition.

The Theory of Groups And Quantum Mechanics

Author : Herman Weyl
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Quantum Theory Groups and Representations

Author : Peter Woit
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This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

The Theory of Groups and Quantum Mechanics

Author : Samuel Clement Bradford
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Gruppentheorie und Quantenmechanik The Theory of Groups and Quantum Mechanics Translated from the Second Revised German Edition by H P Robertson Etc

Author : Hermann Weyl
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Group Theory in Quantum Mechanics

Author : Volker Heine
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Group Theory in Quantum Mechanics: An Introduction to its Present Usage introduces the reader to the three main uses of group theory in quantum mechanics: to label energy levels and the corresponding eigenstates; to discuss qualitatively the splitting of energy levels as one starts from an approximate Hamiltonian and adds correction terms; and to aid in the evaluation of matrix elements of all kinds, and in particular to provide general selection rules for the non-zero ones. The theme is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions. This book is comprised of eight chapters and begins with an overview of the necessary mathematical concepts, including representations and vector spaces and their relevance to quantum mechanics. The uses of symmetry properties and mathematical expression of symmetry operations are also outlined, along with symmetry transformations of the Hamiltonian. The next chapter describes the three uses of group theory, with particular reference to the theory of atomic energy levels and transitions. The following chapters deal with the theory of free atoms and ions; representations of finite groups; the electronic structure and vibrations of molecules; solid state physics; and relativistic quantum mechanics. Nuclear physics is also discussed, with emphasis on the isotopic spin formalism, nuclear forces, and the reactions that arise when the nuclei take part in time-dependent processes. This monograph will be of interest to physicists and mathematicians.

The Theory of Groups and Quantum Mechanics

Author : Hermann Claus Hugo Weyl (Mathematician, Physicist, Germany, Switzerland, United States)
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Quantum Theory Groups Fields and Particles

Author : A. O. Barut
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Symmetry and Dynamics have played, sometimes dualistic, sometimes complimentary, but always a very essential role in the physicist's description and conception of Nature. These are again the basic underlying themes of the present volume. It collects self-contained introductory contributions on some of the recent developments both in mathematical concepts and in physical applications which are becoming very important in current research. So we see in this volume, on the one hand, differential geometry, group representations, topology and algebras and on the other hand, particle equations, particle dynamics and particle interactions. Specifically, this book contains a complete exposition of the theory of deformations of symplectic algebras and quantization, expository material on topology and geometry in physics, and group representations. On the more physical side, we have studies on the concept of particles, on conformal spinors of Cartan, on gauge and supersymmetric field theories, and on relativistic theory of particle interactions and the theory of magnetic resonances. The contributions collected here were originally delivered at two Meetings in Turkey, at Blacksea University in Trabzon and at the University of Bosphorus in Istanbul. But they have been thoroughly revised, updated and extended for this volume. It is a pleasure for me to acknowledge the support of UNESCO, the support and hospitality of Blacksea and Bosphorus Universities for these two memorable Meetings in Mathematical Physics, and to thank the Contributors for their effort and care in preparing this work.

Lie Groups and Quantum Mechanics

Author : D. J. Simms
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Group Theory and Its Application to Physical Problems

Author : Morton Hamermesh
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"A remarkably intelligible survey . . . well organized, well written and very clear throughout." — Mathematical Reviews This excellent text, long considered one of the best-written, most skillful expositions of group theory and its physical applications, is directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. No knowledge of group theory is assumed, but the reader is expected to be familiar with quantum mechanics. And while much of the book concerns theory, readers will nevertheless find a large number of physical applications in the fields of crystallography, molecular theory, and atomic and nuclear physics. The first seven chapters of the book are concerned with finite groups, focusing on the central role of the symmetric group. This section concludes with a chapter dealing with the problem of determining group characters, as it discusses Young tableaux, Yamanouchi symbols, and the method of Hund. The remaining five chapters discuss continuous groups, particularly Lie groups, with the final chapter devoted to the ray representation of Lie groups. The author, Professor Emeritus of Physics at the University of Minnesota, has included a generous selection of problems. They are inserted throughout the text at the place where they naturally arise, making the book ideal for self-study as well as for classroom assignment. 77 illustrations. "A very welcome addition to [the] literature. . . . I would warmly recommend the book to all serious students of Group Theory as applied to Physics." — Contemporary Physics. Index. Bibliography. Problems. Tables.

Groups and Characters

Author : Victor E Hill
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Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. Until now, however, there have been virtually no accessible treatments of group theory that include representations and characters. The classic works in the field require a high level of mathematical sophistication, and other texts omit representations and characters. Groups and Characters offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, this unique text emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The author presents group theory through the Sylow Theorems and includes the full subgroup structure of A5. Representations and characters are worked out with numerous character tables, along with real and induced characters that lead to the table for S5. The text includes specific sections that provide the mathematical basis for some of the important applications of group theory in spectroscopy and molecular structure. It also offers numerous exercises-some stressing computation of concrete examples, others stressing development of the mathematical theory. Groups and Characters provides the ideal grounding for more advanced studies with the classic texts, and for more broad-based work in abstract algebra. Furthermore, physical scientists-whose experience with groups and characters may not be rigorous-will find Groups and Characters the ideal means for gaining a sense of the mathematics lying behind the techniques used in applications.

Group Theory and Physics

Author : S. Sternberg
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A cohesive and well-motivated introduction to group theory and its application to physics.

Representation Theory of Algebraic Groups and Quantum Groups

Author : Akihiko Gyoja
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Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics