Quantum Mechanics Via Lie Algebras
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| Author | : Arnold Neumaier |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 504 |
| Release | : 2024-10-07 |
| Genre | : Science |
| ISBN | : 3110406209 |
This monograph introduces mathematicians, physicists, and engineers to the ideas relating quantum mechanics and symmetries - both described in terms of Lie algebras and Lie groups. The exposition of quantum mechanics from this point of view reveals that classical mechanics and quantum mechanics are very much alike. Written by a mathematician and a physicist, this book is (like a math book) about precise concepts and exact results in classical mechanics and quantum mechanics, but motivated and discussed (like a physics book) in terms of their physical meaning. The reader can focus on the simplicity and beauty of theoretical physics, without getting lost in a jungle of techniques for estimating or calculating quantities of interest.
| Author | : Yair Shapira |
| Publisher | : |
| Total Pages | : 678 |
| Release | : 2021 |
| Genre | : Mechanics |
| ISBN | : 9789811240065 |
| Author | : Howard Georgi |
| Publisher | : Westview Press |
| Total Pages | : 340 |
| Release | : 1999-10-22 |
| Genre | : Science |
| ISBN | : 0738202339 |
An exciting new edition of a classic text
| Author | : Robert Gilmore |
| Publisher | : Cambridge University Press |
| Total Pages | : 5 |
| Release | : 2008-01-17 |
| Genre | : Science |
| ISBN | : 113946907X |
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
| Author | : Jürgen Fuchs |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 1995-03-09 |
| Genre | : Mathematics |
| ISBN | : 9780521484121 |
This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.
| Author | : Peter Woit |
| Publisher | : Springer |
| Total Pages | : 659 |
| Release | : 2017-11-01 |
| Genre | : Science |
| ISBN | : 3319646125 |
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.
| Author | : Francesco Iachello |
| Publisher | : Springer |
| Total Pages | : 208 |
| Release | : 2007-02-22 |
| Genre | : Science |
| ISBN | : 3540362398 |
This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
| Author | : Robert Gilmore |
| Publisher | : Courier Corporation |
| Total Pages | : 610 |
| Release | : 2012-05-23 |
| Genre | : Mathematics |
| ISBN | : 0486131564 |
This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
| Author | : Josi A. de Azcárraga |
| Publisher | : Cambridge University Press |
| Total Pages | : 480 |
| Release | : 1998-08-06 |
| Genre | : Mathematics |
| ISBN | : 9780521597005 |
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
| Author | : Willi-Hans Steeb |
| Publisher | : World Scientific |
| Total Pages | : 208 |
| Release | : 1994 |
| Genre | : Science |
| ISBN | : 9789810217709 |
Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays the labor of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching tasks, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer.This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++.Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented.The level of presentation is such that one can get a sound grasp of computational techniques early on in one's scientific education. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses.
