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Linear Algebra For Quantum Theory

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Linear Algebra For Quantum Theory

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Author : Per-Olov Löwdin
language : en
Publisher: Wiley-Interscience
Release Date : 1998-04-09

Linear Algebra For Quantum Theory written by Per-Olov Löwdin and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-09 with Science categories.

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.

Introduction To Quantum Algorithms Via Linear Algebra Second Edition

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Author : Richard J. Lipton
language : en
Publisher: MIT Press
Release Date : 2021-04-06

Introduction To Quantum Algorithms Via Linear Algebra Second Edition written by Richard J. Lipton and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-06 with Science categories.

Linear Operators For Quantum Mechanics

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Author : Thomas F. Jordan
language : en
Publisher: Courier Corporation
Release Date : 2012-09-20

Linear Operators For Quantum Mechanics written by Thomas F. Jordan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-20 with Science categories.

Suitable for advanced undergraduates and graduate students, this compact treatment examines linear space, functionals, and operators; diagonalizing operators; operator algebras; and equations of motion. 1969 edition.

Quantum Theory Groups And Representations

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Author : Peter Woit
language : en
Publisher: Springer
Release Date : 2017-11-01

Quantum Theory Groups And Representations written by Peter Woit and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-01 with Science categories.

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.

Quantum Mechanics In Simple Matrix Form

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Author : Thomas F. Jordan
language : en
Publisher: Dover Publications
Release Date : 2013-12-11

Quantum Mechanics In Simple Matrix Form written by Thomas F. Jordan and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with categories.

With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Includes more than 100 problems and 38 figures. 1986 edition.

Alice And Bob Meet Banach

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Author : Guillaume Aubrun
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30

Alice And Bob Meet Banach written by Guillaume Aubrun and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Mathematics categories.

The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.

Quantum Algorithms Via Linear Algebra

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Author : Richard J. Lipton
language : en
Publisher: MIT Press
Release Date : 2014-12-05

Quantum Algorithms Via Linear Algebra written by Richard J. Lipton and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Science categories.

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.

An Introduction To Quantum Theory

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Author : Keith Hannabuss
language : en
Publisher: Clarendon Press
Release Date : 1997-03-20

An Introduction To Quantum Theory written by Keith Hannabuss and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-20 with Science categories.

This book provides an introduction to quantum theory primarily for students of mathematics. Although the approach is mainly traditional the discussion exploits ideas of linear algebra, and points out some of the mathematical subtleties of the theory. Amongst the less traditional topics are Bell's inequalities, coherent and squeezed states, and introductions to group representation theory. Later chapters discuss relativistic wave equations and elementary particle symmetries from a group theoretical standpoint rather than the customary Lie algebraic approach. This book is intended for the later years of an undergraduate course or for graduates. It assumes a knowledge of basic linear algebra and elementary group theory, though for convenience these are also summarized in an appendix.

Mathematics Of Classical And Quantum Physics

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Author : Frederick W. Byron
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26

Mathematics Of Classical And Quantum Physics written by Frederick W. Byron and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Science categories.

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Linear Algebra Problem Book

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Author : Paul R. Halmos
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-12-31

Linear Algebra Problem Book written by Paul R. Halmos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-31 with Mathematics categories.

Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.

Linear Algebra For Quantum Theory

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