1 < \- * – 1 * r * – • *r = (Üt) = (#0 '*) = i, "U", " - #0% 5 Vf (1 + f1) VW = pff, Ü f: (1 + f1) U-'V4, Furthermore, f(f; + if) = 1 + f is valid. We commute U with f, to give Ü f = (E, + moc") 1 + f1 (Ep – moc”) f; – 4: (E, ...

Author: Walter Greiner

Publisher: Springer Science & Business Media

ISBN: 9783662042755

Category: Science

Page: 424

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Relativistic Quantum Mechanics. Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course. This third edition has been slightly revised to bring the text up-to-date.

Selected Topics with Computer-Generated Animations of Quantum-Mechanical Phenomena Bernd Thaller ... Quantum Mechanics on the Macintosh, and Quantum Mechanics on the Personal Computer. 2nd edition. ... [16] R. Eisberg, R. Resnick.

Author: Bernd Thaller

Publisher: Springer Science & Business Media

ISBN: 9780387227702

Category: Science

Page: 283

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"Visual Quantum Mechanics" uses the computer-generated animations found on the accompanying material on Springer Extras to introduce, motivate, and illustrate the concepts explained in the book. While there are other books on the market that use Mathematica or Maple to teach quantum mechanics, this book differs in that the text describes the mathematical and physical ideas of quantum mechanics in the conventional manner. There is no special emphasis on computational physics or requirement that the reader know a symbolic computation package. Despite the presentation of rather advanced topics, the book requires only calculus, making complicated results more comprehensible via visualization. The material on Springer Extras provides easy access to more than 300 digital movies, animated illustrations, and interactive pictures. This book along with its extra online materials forms a complete introductory course on spinless particles in one and two dimensions.

A Primer in Theoretical Physics with Fractals for the Macintosh (R) Dietrich Stauffer, H. Eugene Stanley. 3. Quantum Mechanics The theory of relativity has already shaken the foundations of our understanding of the natural world: two ...

Author: Dietrich Stauffer

Publisher: Springer

ISBN: 9783642867804

Category: Science

Page: 211

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From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a diskette where a selection of executable programs exploring the fractal concept can be found.

With Applications in Condensed Matter and Atomic Physics Paul Strange ... The radial Klein - Gordon equation is ( W – V ( r ) ) 2r2 + ( 3.103 ) c2 R ( r ) ar ar and a little rearrangement gives 2R ( r ) 2 aR ( r ) ( W – V ( r ) ) 2 mac ...

Author: Paul Strange

Publisher: Cambridge University Press

ISBN: 0521565839

Category: Science

Page: 614

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This graduate text introduces relativistic quantum theory, emphasising its important applications in condensed matter physics. Relativistic quantum theory is the unification into a consistent theory of Einstein's theory of relativity and the quantum mechanics of Bohr, Schrödinger, and Heisenberg, etc. Beginning with basic theory, the book then describes essential topics. Many worked examples and exercises are included along with an extensive reference list. This clear account of a crucial topic in science will be valuable to graduates and researchers working in condensed matter physics and quantum physics.

We denote by R the set of Rajchman measures. By Proposition C.25 of App. C, the Lebesgue ... in R. We have [175]: Mac(R) ⊊ R ⊊ Mc(R), (3.109) where Mac (respectively, Mc) denote the set of a.c. (respectively, continuous) measures.

Author: Domingos H. U. Marchetti

Publisher: World Scientific

ISBN: 9789814383813

Category: Science

Page: 362

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Time decays form the basis of a multitude of important and interesting phenomena in quantum physics that range from spectral properties, resonances, return and approach to equilibrium, to quantum mixing, dynamical stability properties and irreversibility and the OC arrow of timeOCO.This monograph is devoted to a clear and precise, yet pedagogical account of the associated concepts and methods.

From Eqs . ( 1-92 ) and ( 1-93 ) the relative Hamiltonian is pa ei ez el / 4 ežui Hrel = + + 2m mica ' maca eil2 e2Mi 02 · L + o ( 1-100 ) mic mac + ( r with p2 = -t'r - 2Ər ( r20r ) + r - 2L ?. Note that this Hamiltonian is both ...

Author: W.T. Grandy

Publisher: Springer Science & Business Media

ISBN: 0792310497

Category: Science

Page: 458

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The material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study.

Towards a Theory of Scale Relativity Laurent Nottale ... Schiff , L.I. , Quantum Mechanics ( Mac Graw Hill , 1968 ) . 25. Feynman , R.P. , Leighton , R. , & Sands , M. , The Feynman Lectures on Physics ( Addison - Wesley , 1964 ) . 26.

Author: Laurent Nottale

Publisher: World Scientific

ISBN: 9810208782

Category: Science

Page: 358

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This is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.

Sharp and Unsharp Quantum Logics Maria Luisa Dalla Chiara, Roberto Giuntini, Richard Greechie ... Thus, by a theorem proved by MacLaren (Kalmbach, 1983), the Mac Neille completion of C(C0(2)(R)) is isomorphic to the Mac Neille ...

Author: Maria Luisa Dalla Chiara

Publisher: Springer Science & Business Media

ISBN: 9789401705264

Category: Mathematics

Page: 298

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"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking. For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.

M.J. Klein, Max Planck and the beginnings of the quantum theory. AHES 1 (1960—2). R. MacCormmach, The atomic theory of John William Nicholson. AHES 3 (1966-7). R. Mac Cormmach, H.A. Lorentz and the electromagnetic view of nature.

Author: Alex Keller

Publisher: Courier Corporation

ISBN: 9780486149950

Category: Science

Page: 240

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This compelling history portrays the human faces and lives behind the beginnings of atomic science, from experiments in the 1880s to the era just after the First World War.

[139] R. Landauer. Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5 (1961), 183–91. [140] G. Ludwig. An Axiomatic Basis of Quantum Mechanics. 1. ... [145] S. Mac Lane. Homology.

Author: Hans Halvorson

Publisher: Cambridge University Press

ISBN: 9781139499224

Category: Mathematics

Page:

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No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.