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Quantum Mechanics Using Computer Algebra

Author: Willi-Hans Steeb

Publisher: World Scientific

Published: 1994

Total Pages: 208

ISBN-13: 9789810217709

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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.

Book Synopsis Quantum Mechanics Using Computer Algebra by : Willi-Hans Steeb

Download or read book Quantum Mechanics Using Computer Algebra written by Willi-Hans Steeb and published by World Scientific. This book was released on 1994 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Mechanics Using Computer Algebra

Author: Willi-Hans Steeb

Publisher: World Scientific Publishing Company

Published: 2010-03-24

Total Pages: 244

ISBN-13: 9813107898

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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.

Book Synopsis Quantum Mechanics Using Computer Algebra by : Willi-Hans Steeb

Download or read book Quantum Mechanics Using Computer Algebra written by Willi-Hans Steeb and published by World Scientific Publishing Company. This book was released on 2010-03-24 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: W.-H. Steeb

Publisher: World Scientific Publishing Company Incorporated

Published: 2010

Total Pages: 234

ISBN-13: 9789814307161

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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 explantory 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++. --

Book Synopsis Quantum Mechanics Using Computer Algebra by : W.-H. Steeb

Download or read book Quantum Mechanics Using Computer Algebra written by W.-H. Steeb and published by World Scientific Publishing Company Incorporated. This book was released on 2010 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 explantory 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++. --

Quantum Mechanics Using Computer Algebra

Author: Willi-hans Steeb

Publisher:

Published: 1994

Total Pages: 201

ISBN-13: 9789814447041

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Book Synopsis Quantum Mechanics Using Computer Algebra by : Willi-hans Steeb

Download or read book Quantum Mechanics Using Computer Algebra written by Willi-hans Steeb and published by . This book was released on 1994 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computer Algebra in Quantum Field Theory

Author: Carsten Schneider

Publisher: Springer Science & Business Media

Published: 2013-10-05

Total Pages: 422

ISBN-13: 3709116163

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The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

Book Synopsis Computer Algebra in Quantum Field Theory by : Carsten Schneider

Download or read book Computer Algebra in Quantum Field Theory written by Carsten Schneider and published by Springer Science & Business Media. This book was released on 2013-10-05 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

Quantum Mechanics Using Computer Algebra

Author: W.-H. Steeb

Publisher: World Scientific

Published: 2010

Total Pages: 245

ISBN-13: 9814307173

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Book Synopsis Quantum Mechanics Using Computer Algebra by : W.-H. Steeb

Download or read book Quantum Mechanics Using Computer Algebra written by W.-H. Steeb and published by World Scientific. This book was released on 2010 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 explantory 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++. --

Quantum Mechanics Using Maple ®

Author: Marko Horbatsch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 343

ISBN-13: 3642795382

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Quantum Mechanics Using Maple permits the study of quantum mechanics in a novel, interactive way using the computer algebra and graphics system Maple V. Usually the physics student is distracted from understanding the concepts of modern physics by the need to master unfamiliar mathematics at the same time. In 39 guided Maple sessions the reader explores many standard quantum mechanics problems, as well as some advanced topics that introduce approximation techniques. A solid knowledge of Maple V is acquired as it applies to advanced mathematics relevant for engineering, physics, and applied mathematics. The diskette contains 39 Maple V for Windows worksheet files to reproduce all the problems presented in the text. The suggested exercises can be performed with a minimum of typing.

Book Synopsis Quantum Mechanics Using Maple ® by : Marko Horbatsch

Download or read book Quantum Mechanics Using Maple ® written by Marko Horbatsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Mechanics Using Maple permits the study of quantum mechanics in a novel, interactive way using the computer algebra and graphics system Maple V. Usually the physics student is distracted from understanding the concepts of modern physics by the need to master unfamiliar mathematics at the same time. In 39 guided Maple sessions the reader explores many standard quantum mechanics problems, as well as some advanced topics that introduce approximation techniques. A solid knowledge of Maple V is acquired as it applies to advanced mathematics relevant for engineering, physics, and applied mathematics. The diskette contains 39 Maple V for Windows worksheet files to reproduce all the problems presented in the text. The suggested exercises can be performed with a minimum of typing.

Quantum Methods with Mathematica®

Author: James F. Feagin

Publisher: Springer Science & Business Media

Published: 2002-01-08

Total Pages: 508

ISBN-13: 9780387953656

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Feagin's book was the first publication dealing with Quantum Mechanics using Mathematica, the popular software distributed by Wolfram Research, and designed to facilitate scientists and engineers to do difficult scientific computations more quickly and more easily. Quantum Methods with Mathematica, the first book of ist kind, has achieved worldwide success and critical acclaim.

Book Synopsis Quantum Methods with Mathematica® by : James F. Feagin

Download or read book Quantum Methods with Mathematica® written by James F. Feagin and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Feagin's book was the first publication dealing with Quantum Mechanics using Mathematica, the popular software distributed by Wolfram Research, and designed to facilitate scientists and engineers to do difficult scientific computations more quickly and more easily. Quantum Methods with Mathematica, the first book of ist kind, has achieved worldwide success and critical acclaim.

Linear Algebra for Quantum Theory

Author: Per-Olov Löwdin

Publisher: Wiley-Interscience

Published: 1998-04-09

Total Pages: 0

ISBN-13: 9780471199588

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Essential mathematical tools for the study of modern quantumtheory. Linear Algebra for Quantum Theory offers an excellent survey ofthose aspects of set theory and the theory of linear spaces andtheir mappings that are indispensable to the study of quantumtheory. Unlike more conventional treatments, this text postponesits discussion of the binary product concept until later chapters,thus allowing many important properties of the mappings to bederived without it. The book begins with a thorough exploration of set theoryfundamentals, including mappings, cardinalities of sets, andarithmetic and theory of complex numbers. Next is an introductionto linear spaces, with coverage of linear operators, eigenvalue andthe stability problem of linear operators, and matrices withspecial properties. Material on binary product spaces features self-adjoint operatorsin a space of indefinite metric, binary product spaces with apositive definite metric, properties of the Hilbert space, andmore. The final section is devoted to axioms of quantum theoryformulated as trace algebra. Throughout, chapter-end problem setshelp reinforce absorption of the material while letting readerstest their problem-solving skills. Ideal for advanced undergraduate and graduate students intheoretical and computational chemistry and physics, Linear Algebrafor Quantum Theory provides the mathematical means necessary toaccess and understand the complex world of quantum theory.

Book Synopsis Linear Algebra for Quantum Theory by : Per-Olov Löwdin

Download or read book Linear Algebra for Quantum Theory written by Per-Olov Löwdin and published by Wiley-Interscience. This book was released on 1998-04-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential mathematical tools for the study of modern quantumtheory. Linear Algebra for Quantum Theory offers an excellent survey ofthose aspects of set theory and the theory of linear spaces andtheir mappings that are indispensable to the study of quantumtheory. Unlike more conventional treatments, this text postponesits discussion of the binary product concept until later chapters,thus allowing many important properties of the mappings to bederived without it. The book begins with a thorough exploration of set theoryfundamentals, including mappings, cardinalities of sets, andarithmetic and theory of complex numbers. Next is an introductionto linear spaces, with coverage of linear operators, eigenvalue andthe stability problem of linear operators, and matrices withspecial properties. Material on binary product spaces features self-adjoint operatorsin a space of indefinite metric, binary product spaces with apositive definite metric, properties of the Hilbert space, andmore. The final section is devoted to axioms of quantum theoryformulated as trace algebra. Throughout, chapter-end problem setshelp reinforce absorption of the material while letting readerstest their problem-solving skills. Ideal for advanced undergraduate and graduate students intheoretical and computational chemistry and physics, Linear Algebrafor Quantum Theory provides the mathematical means necessary toaccess and understand the complex world of quantum theory.

Quantum Algorithms via Linear Algebra

Author: Richard J. Lipton

Publisher: MIT Press

Published: 2014-12-05

Total Pages: 207

ISBN-13: 0262028395

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Quantum computing explained in terms of elementary linear algebra, emphasizing computation and algorithms and requiring no background in physics. This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, this primer makes quantum algorithms accessible to students and researchers in computer science without the complications of quantum mechanical notation, physical concepts, and philosophical issues. After explaining the development of quantum operations and computations based on linear algebra, the book presents the major quantum algorithms, from seminal algorithms by Deutsch, Jozsa, and Simon through Shor's and Grover's algorithms to recent quantum walks. It covers quantum gates, computational complexity, and some graph theory. Mathematical proofs are generally short and straightforward; quantum circuits and gates are used to illuminate linear algebra; and the discussion of complexity is anchored in computational problems rather than machine models. Quantum Algorithms via Linear Algebra is suitable for classroom use or as a reference for computer scientists and mathematicians.

Book Synopsis Quantum Algorithms via Linear Algebra by : Richard J. Lipton

Download or read book Quantum Algorithms via Linear Algebra written by Richard J. Lipton and published by MIT Press. This book was released on 2014-12-05 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computing explained in terms of elementary linear algebra, emphasizing computation and algorithms and requiring no background in physics. This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, this primer makes quantum algorithms accessible to students and researchers in computer science without the complications of quantum mechanical notation, physical concepts, and philosophical issues. After explaining the development of quantum operations and computations based on linear algebra, the book presents the major quantum algorithms, from seminal algorithms by Deutsch, Jozsa, and Simon through Shor's and Grover's algorithms to recent quantum walks. It covers quantum gates, computational complexity, and some graph theory. Mathematical proofs are generally short and straightforward; quantum circuits and gates are used to illuminate linear algebra; and the discussion of complexity is anchored in computational problems rather than machine models. Quantum Algorithms via Linear Algebra is suitable for classroom use or as a reference for computer scientists and mathematicians.