Algebraic Methods In Quantum Chemistry And Physics
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Algebraic Methods In Quantum Chemistry And Physics
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Author : Francisco M. Fernandez
language : en
Publisher: CRC Press
Release Date : 2020-01-16
Algebraic Methods In Quantum Chemistry And Physics written by Francisco M. Fernandez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Mathematics categories.
Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.
Geometric And Algebraic Topological Methods In Quantum Mechanics
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Author : Luigi Mangiarotti
language : en
Publisher: World Scientific
Release Date : 2005-01-27
Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-27 with Science categories.
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Mathematical Models And Methods For Ab Initio Quantum Chemistry
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Author : M. Defranceschi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Models And Methods For Ab Initio Quantum Chemistry written by M. Defranceschi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.
Algebraic And Diagrammatic Methods In Many Fermion Theory
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Author : Frank E. Harris
language : en
Publisher: Courier Dover Publications
Release Date : 2020-01-15
Algebraic And Diagrammatic Methods In Many Fermion Theory written by Frank E. Harris and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Science categories.
This text on the use of electron correlation effects in the description of the electronic structure of atoms, molecules, and crystals is intended for graduate students in physical chemistry and physics. Modern theories of electronic structure and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation, and the methods developed in the text are illustrated with examples from molecular and solid state quantum mechanics. A brief Introduction is followed by chapters on operator algebra, the independent-particle model, occupation-number formalism, and diagrams. Additional topics include the configuration-interaction method, the many-body perturbation theory, and the coupled-cluster method.
Algebraic Approach To Simple Quantum Systems
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Author : Barry G. Adams
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Approach To Simple Quantum Systems written by Barry G. Adams and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book provides an introduction to the use of algebraic methods and sym bolic computation for simple quantum systems with applications to large order perturbation theory. It is the first book to integrate Lie algebras, algebraic perturbation theory and symbolic computation in a form suitable for students and researchers in theoretical and computational chemistry and is conveniently divided into two parts. The first part, Chapters 1 to 6, provides a pedagogical introduction to the important Lie algebras so(3), so(2,1), so(4) and so(4,2) needed for the study of simple quantum systems such as the D-dimensional hydrogen atom and harmonic oscillator. This material is suitable for advanced undergraduate and beginning graduate students. Of particular importance is the use of so(2,1) in Chapter 4 as a spectrum generating algebra for several important systems such as the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This approach provides an interesting and important alternative to the usual textbook approach using series solutions of differential equations.
Factorization Method In Quantum Mechanics
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Author : Shi-Hai Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-01
Factorization Method In Quantum Mechanics written by Shi-Hai Dong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-01 with Science categories.
This book introduces the factorization method in quantum mechanics at an advanced level, with the aim of putting mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader’s disposal. For this purpose, the text provides a comprehensive description of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in quantum mechanics textbooks.
Ab Initio Methods In Quantum Chemistry Volume 67 Part 1
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Author : K. P. Lawley
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-08
Ab Initio Methods In Quantum Chemistry Volume 67 Part 1 written by K. P. Lawley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-08 with Science categories.
The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.
Algebraic Methods In Quantum Chemistry And Physics
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Author : Francisco M. Fernandez
language : en
Publisher: CRC Press
Release Date : 2020-01-16
Algebraic Methods In Quantum Chemistry And Physics written by Francisco M. Fernandez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Mathematics categories.
Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.
Quantum Mechanics Using Computer Algebra
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Author : Willi-Hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 2010-03-24
Quantum Mechanics Using Computer Algebra written by Willi-Hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-24 with Mathematics categories.
Solving problems in quantum mechanics is an essential skill and research activity for physicists, mathematicians, engineers and others. Nowadays, the labor of scientific computation has been greatly eased by the advent of computer algebra packages, which do not merely perform number crunching, but also enable users to manipulate algebraic expressions and equations symbolically. For example, the manipulations of noncommutative operators, differentiation and integration can now be carried out algebraically by the computer algebra package. This book collects standard and advanced methods in quantum mechanics and implements them using SymbolicC++ and Maxima, two popular computer algebra packages. Throughout, the sample programs and their outputs are accompanied with explanatory text of the underlying mathematics and physics explained in detail. Selected problems have also been implemented using two other popular packages — Mathematica and Maple — while some problems are implemented in C++. Modern developments in quantum theory are covered extensively, beyond the standard quantum mechanical techniques. The new research topics added to this second edition are: entanglement, teleportation, Berry phase, Morse oscillator, Magnus expansion, wavelets, Pauli and Clifford groups, coupled Bose–Fermi systems, super-Lie algebras, etc.
Quantum Mechanics Using Computer Algebra
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Author : Willi-Hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 1994-05-23
Quantum Mechanics Using Computer Algebra written by Willi-Hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-23 with Science categories.
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.