Exact Solutions of Relativistic Wave Equations
Exact Solutions of Relativistic Wave Equations

Author: V.G. Bagrov

Publisher: Springer Science & Business Media

Published: 1990-02-28

Total Pages: 342

ISBN-13: 9780792302155

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'Et moi * .... si favait su comment en revenir. One service mathematics bllS rendered the je n'y serais point aile.' human race. It hal put common sense back Jules Verne where it bdongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense', able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thOUght. A highly necessary tool in a world where both feedback and non­ Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Wave Equations in Higher Dimensions
Wave Equations in Higher Dimensions

Author: Shi-Hai Dong

Publisher: Springer Science & Business Media

Published: 2011-07-09

Total Pages: 299

ISBN-13: 9400719175

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Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.

Exact Solutions of Einstein's Field Equations
Exact Solutions of Einstein's Field Equations

Author: Hans Stephani

Publisher: Cambridge University Press

Published: 2009-09-24

Total Pages: 732

ISBN-13: 9780521467025

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A completely revised and updated edition of this classic text, covering important new methods and many recently discovered solutions. This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics
Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

Author: W.I. Fushchich

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 456

ISBN-13: 9401731985

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by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.

Relativity and the Dimensionality of the World
Relativity and the Dimensionality of the World

Author: Vesselin Petkov

Publisher: Springer Science & Business Media

Published: 2007-10-08

Total Pages: 283

ISBN-13: 1402063180

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The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? The book contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it.

Progress in Materials Science Research
Progress in Materials Science Research

Author: Antonio C. Venetti

Publisher: Nova Publishers

Published: 2008

Total Pages: 256

ISBN-13: 9781600216336

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Materials science includes those parts of chemistry and physics that deal with the properties of materials. It encompasses four classes of materials, the study of each of which may be considered a separate field: metals; ceramics; polymers and composites. Materials science is often referred to as materials science and engineering because it has many applications. Industrial applications of materials science include processing techniques (casting, rolling, welding, ion implantation, crystal growth, thin-film deposition, sintering, glassblowing, etc.), analytical techniques (electron microscopy, x-ray diffraction, calorimetry, nuclear microscopy (HEFIB) etc.), materials design, and cost/benefit tradeoffs in industrial production of materials. This new volume gathers important research from around the globe in this dynamic field.

The Dirac Equation and its Solutions
The Dirac Equation and its Solutions

Author: Vladislav G. Bagrov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-08-20

Total Pages: 557

ISBN-13: 3110377756

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The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In this monograph, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

Quantum Information in Gravitational Fields
Quantum Information in Gravitational Fields

Author: Marco Lanzagorta

Publisher: Morgan & Claypool Publishers

Published: 2014-06-01

Total Pages: 481

ISBN-13: 1627056017

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One of the major scientific thrusts in recent years has been to try to harness quantum phenomena to increase dramatically the performance of a wide variety of classical information processing devices. In particular, it is generally accepted that quantum co

Computational Strong-Field Quantum Dynamics
Computational Strong-Field Quantum Dynamics

Author: Dieter Bauer

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2017-04-24

Total Pages: 290

ISBN-13: 311041726X

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This graduate textbook introduces the com-putational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time dependent Schrödinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach. Contents How to propagate a wavefunction? Calculation of typical strong-field observables Time-dependent relativistic wave equations: Numerics of the Dirac and the Klein-Gordon equation Time-dependent density functional theory The multiconfiguration time-dependent Hartree-Fock method Time-dependent configuration interaction singles Strong-field approximation and quantum orbits Microscopic particle-in-cell approach