Group Theory And Quantum Mechanics

Group Theory and Quantum Mechanics PDF
Author: Michael Tinkham
Publisher: Courier Corporation
ISBN: 0486131661
Size: 71.77 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 352
View: 2937

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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

Group Theory PDF
Author: Eugene P. Wigner
Publisher: Elsevier
ISBN: 1483275760
Size: 80.43 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 384
View: 1785

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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.

The Theory Of Groups And Quantum Mechanics

The Theory of Groups and Quantum Mechanics PDF
Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 9780486602691
Size: 20.88 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 422
View: 7339

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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.

Applications Of Group Theory In Quantum Mechanics

Applications of Group Theory in Quantum Mechanics PDF
Author: M. I. Petrashen
Publisher: Courier Corporation
ISBN: 0486172724
Size: 73.48 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 336
View: 7216

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Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications. The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.

Group Theory And Quantum Mechanics

Group Theory and Quantum Mechanics PDF
Author: Bartel L. van der Waerden
Publisher: Springer Science & Business Media
ISBN: 3642658601
Size: 25.30 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 211
View: 7714

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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.

Group Theory In Physics

Group Theory in Physics PDF
Author: Wu-Ki Tung
Publisher: World Scientific Publishing Company
ISBN: 981310404X
Size: 58.60 MB
Format: PDF, Docs
Category : Representations of groups
Languages : en
Pages : 336
View: 7186

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An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy

Group Theory And Its Application To Physical Problems

Group Theory and Its Application to Physical Problems PDF
Author: Morton Hamermesh
Publisher: Courier Corporation
ISBN: 0486140393
Size: 12.75 MB
Format: PDF, ePub
Category : Science
Languages : en
Pages : 544
View: 2434

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One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.

Group Theory In Quantum Mechanics

Group Theory in Quantum Mechanics PDF
Author: Volker Heine
Publisher: Elsevier
ISBN: 1483152006
Size: 18.10 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 478
View: 4057

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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.

Quantum Theory Groups And Representations

Quantum Theory  Groups and Representations PDF
Author: Peter Woit
Publisher: Springer
ISBN: 3319646125
Size: 65.83 MB
Format: PDF
Category : Science
Languages : en
Pages : 668
View: 6007

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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.