Quantum Mechanics for Mathematicians

Author: Leon Armenovich Takhtadzhi͡an

Publisher: American Mathematical Soc.

ISBN: 0821846302

Category: Mathematics

Page: 387

View: 7481

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This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results.Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.

Mathematical Methods of Classical Mechanics

Author: V.I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 9780387968902

Category: Mathematics

Page: 520

View: 2402

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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Foundations of Mechanics

Author: Ralph Abraham,Jerrold E. Marsden

Publisher: American Mathematical Soc.

ISBN: 0821844385

Category: Mathematics

Page: 826

View: 567

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Undoubtedly [the book] will be for years the standard reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics. --Zentralblatt fur Mathematik For many years, this book has been viewed as a classic treatment of geometric mechanics. It is known for its broad exposition of the subject, with many features that cannot be found elsewhere. The book is recommended as a textbook and as a basic reference work for the foundations of differentiable and Hamiltonian dynamics.

The Mathematical Principles of Quantum Mechanics

Author: Derek F. Lawden

Publisher: Courier Corporation

ISBN: 0486442233

Category: Science

Page: 280

View: 5513

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Focusing on the principles of quantum mechanics, this text for upper-level undergraduates and graduate students introduces and resolves special physical problems with more than 100 exercises. 1967 edition.

A History of Mechanics

Author: René Dugas

Publisher: Courier Corporation

ISBN: 0486173372

Category: Science

Page: 688

View: 4831

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Monumental study traces the history of mechanical principles chronologically from antiquity through the early 20th century. Contributions of ancient Greeks, Leonardo, Galileo, Kepler, Lagrange, others. 116 illustrations.

The Variational Principles of Mechanics

Author: Cornelius Lanczos

Publisher: Courier Corporation

ISBN: 0486134709

Category: Science

Page: 464

View: 2389

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Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Lectures on Quantum Mechanics for Mathematics Students

Author: L. D. Faddeev,Oleg Aleksandrovich I︠A︡kubovskiĭ

Publisher: American Mathematical Soc.

ISBN: 082184699X

Category: Science

Page: 234

View: 7850

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Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.

Rigid Body Mechanics

Mathematics, Physics and Applications

Author: William B. Heard

Publisher: John Wiley & Sons

ISBN: 3527618821

Category: Science

Page: 262

View: 7062

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This textbook is a modern, concise and focused treatment of the mathematical techniques, physical theories and applications of rigid body mechanics, bridging the gap between the geometric and more classical approaches to the topic. It emphasizes the fundamentals of the subject, stresses the importance of notation, integrates the modern geometric view of mechanics and offers a wide variety of examples -- ranging from molecular dynamics to mechanics of robots and planetary rotational dynamics. The author has unified his presentation such that applied mathematicians, mechanical and astro-aerodynamical engineers, physicists, computer scientists and astronomers can all meet the subject on common ground, despite their diverse applications. * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Classical Mechanics

Author: John Robert Taylor

Publisher: University Science Books

ISBN: 9781891389221

Category: Science

Page: 786

View: 6626

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'Classical Mechanics' is intended for students who have studied some mechanics in an introductory physics course. A particular highlight is the chapter on chaos, which focuses on a few simple systems to give truly comprehensible coverage.

Symmetry in Mechanics

A Gentle, Modern Introduction

Author: Stephanie Frank Singer

Publisher: Springer Science & Business Media

ISBN: 1461201896

Category: Mathematics

Page: 193

View: 6744

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"And what is the use," thought Alice, "of a book without pictures or conversations in it?" -Lewis Carroll This book is written for modem undergraduate students - not the ideal stu dents that mathematics professors wish for (and who occasionally grace our campuses), but the students like many the author has taught: talented but ap preciating review and reinforcement of past course work; willing to work hard, but demanding context and motivation for the mathematics they are learning. To suit this audience, the author eschews density of topics and efficiency of presentation in favor of a gentler tone, a coherent story, digressions on mathe maticians, physicists and their notations, simple examples worked out in detail, and reinforcement of the basics. Dense and efficient texts play a crucial role in the education of budding (and budded) mathematicians and physicists. This book does not presume to improve on the classics in that genre. Rather, it aims to provide those classics with a large new generation of appreciative readers. This text introduces some basic constructs of modern symplectic geometry in the context of an old celestial mechanics problem, the two-body problem. We present the derivation of Kepler's laws of planetary motion from Newton's laws of gravitation, first in the style of an undergraduate physics course, and x Preface then again in the language of symplectic geometry. No previous exposure to symplectic geometry is required: we introduce and illustrate all necessary con structs.

Classical Mechanics

Kinematics and Statics

Author: Jan Awrejcewicz

Publisher: Springer Science & Business Media

ISBN: 1461437911

Category: Science

Page: 440

View: 2817

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This is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.

Classical Mechanics

Transformations, Flows, Integrable and Chaotic Dynamics

Author: Joseph L. McCauley

Publisher: Cambridge University Press

ISBN: 9780521578820

Category: Science

Page: 469

View: 1363

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An advanced text for first-year graduate students in physics and engineering taking a standard classical mechanics course, this is the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability. It introduces flows in phase space and transformations early and illustrates their applications throughout the text. The standard integrable problems of elementary physics are analyzed from the standpoint of flows, transformations, and integrability. This approach allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

Feynman Lectures On Computation

Author: Richard P. Feynman

Publisher: CRC Press

ISBN: 0429980078

Category: Science

Page: 324

View: 5373

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When, in 1984?86, Richard P. Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman, the course also featured, as occasional guest speakers, some of the most brilliant men in science at that time, including Marvin Minsky, Charles Bennett, and John Hopfield. Although the lectures are now thirteen years old, most of the material is timeless and presents a ?Feynmanesque? overview of many standard and some not-so-standard topics in computer science such as reversible logic gates and quantum computers.

Quantum Theory for Mathematicians

Author: Brian C. Hall

Publisher: Springer Science & Business Media

ISBN: 1461471168

Category: Science

Page: 554

View: 3941

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Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

Classical Mechanics

Author: R. Douglas Gregory

Publisher: Cambridge University Press

ISBN: 1139450042

Category: Science

Page: N.A

View: 5299

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Gregory's Classical Mechanics is a major new textbook for undergraduates in mathematics and physics. It is a thorough, self-contained and highly readable account of a subject many students find difficult. The author's clear and systematic style promotes a good understanding of the subject: each concept is motivated and illustrated by worked examples, while problem sets provide plenty of practice for understanding and technique. Computer assisted problems, some suitable for projects, are also included. The book is structured to make learning the subject easy; there is a natural progression from core topics to more advanced ones and hard topics are treated with particular care. A theme of the book is the importance of conservation principles. These appear first in vectorial mechanics where they are proved and applied to problem solving. They reappear in analytical mechanics, where they are shown to be related to symmetries of the Lagrangian, culminating in Noether's theorem.

The Mathematical Mechanic

Using Physical Reasoning to Solve Problems

Author: Mark Levi

Publisher: Princeton University Press

ISBN: 0691154562

Category: Science

Page: 186

View: 5110

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In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

Quantum Mechanics in Hilbert Space

Second Edition

Author: Eduard Prugovecki

Publisher: Courier Corporation

ISBN: 0486318052

Category: Science

Page: 720

View: 6169

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A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas. This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the gap between strictly physics- and mathematics-oriented texts on Hilbert space theory as applied to nonrelativistic quantum mechanics. Organized in the form of definitions, theorems, and proofs of theorems, it allows readers to immediately grasp the basic concepts and results. Exercises appear throughout the text, with hints and solutions at the end.

Approximating Perfection

A Mathematician's Journey into the World of Mechanics

Author: Leonid P. Lebedev,Michael J. Cloud

Publisher: Princeton University Press

ISBN: 1400873258

Category: Mathematics

Page: 232

View: 3097

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This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences. Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience.

Lectures on Fluid Mechanics

Author: Marvin Shinbrot

Publisher: Courier Corporation

ISBN: 0486267962

Category: Science

Page: 240

View: 2667

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Readable and user-friendly, this high-level introduction explores the derivation of the equations of fluid motion from statistical mechanics, classical theory, and a portion of the modern mathematical theory of viscous, incompressible fluids. 1973 edition.