Exact Solutions Of Relativistic Wave Equations
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Exact Solutions Of Relativistic Wave Equations
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Author : V.G. Bagrov
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-02-28
Exact Solutions Of Relativistic Wave Equations written by V.G. Bagrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-02-28 with Science categories.
'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.
Exact Solutions Of Relativistic Wave Equations
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Author : V.G. Bagrov
language : en
Publisher: Springer
Release Date : 1990-03-14
Exact Solutions Of Relativistic Wave Equations written by V.G. Bagrov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-14 with Science categories.
The Dirac Equation And Its Solutions
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Author : Vladislav G. Bagrov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-20
The Dirac Equation And Its Solutions written by Vladislav G. Bagrov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Science categories.
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.
Wave Equations In Higher Dimensions
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Author : Shi-Hai Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-09
Wave Equations In Higher Dimensions written by Shi-Hai Dong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-09 with Science categories.
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.
Relativistic Wave Equations And The Equations Of Motion
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Author : John Sanders
language : en
Publisher:
Release Date : 1964
Relativistic Wave Equations And The Equations Of Motion written by John Sanders and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
"Many theories have been advanced which avoid the difficulties of the Maxwell Electrodynamics; most of these have been quite successful classically, but present difficulties upon quantization. The theory that will be discussed here is a linear one which is closely related to those of Feynman (1) and Lehmann (2), and which is perhaps more easily adaptable to a quantum theory than to a classical one. [...]" --
Symmetry Analysis And Exact Solutions Of Equations Of Nonlinear Mathematical Physics
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Author : W.I. Fushchich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Symmetry Analysis And Exact Solutions Of Equations Of Nonlinear Mathematical Physics written by W.I. Fushchich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
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.
The Pauli Lubanski Vector In A Group Theoretical Approach To Relativistic Wave Equations
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Author : Nathan A. Lanfear
language : en
Publisher:
Release Date : 2016
The Pauli Lubanski Vector In A Group Theoretical Approach To Relativistic Wave Equations written by Nathan A. Lanfear and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Electrodynamics categories.
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,representation theory of the Lorentz and Poincare groups, and a review of some basic rela- tivistic wave equations that will play an important role in the work to follow. In Chapter 2,a complex covariant form of the classical Maxwells equations in a moving medium or atrest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentumtensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and itsconnection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- netic field, E+ iH. To this end, a complex covariant form of Maxwells equations is used.Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Diracsequation, Weyls two-component equation for massless neutrinos and the Proca, Maxwelland Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir operators of the Poincare group. A connection between the spin of a particle/field and consistency of the corresponding overdetermined system is emphasized in the masslesscase. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, whichis a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time evolution of exact wave functions of the generalized harmonic oscillators is determinedin terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it isshown that the classical Arnold transform is naturally connected with Ehrenfests theoremfor generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of themethods introduced in Chapter 5 a model for the quantization of an electromagnetic fieldin a variable media is analyzed. The concept of quantization of an electromagnetic fieldin factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single modeof radiation for this model is used to find time-dependent photon amplitudes in relationto Fock states. A multi-parameter family of the squeezed states, photon statistics, and theuncertainty relation, are explicitly given in terms of the Ermakov-type system.
Relativistic Theory Of Atoms And Molecules
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Author : Pekka Pyykkö
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Relativistic Theory Of Atoms And Molecules written by Pekka Pyykkö and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Exact Solutions For Relativistic Models
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Author : Sifiso Allan Ngubelanga
language : en
Publisher:
Release Date : 2011
Exact Solutions For Relativistic Models written by Sifiso Allan Ngubelanga and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Differential equations categories.
Progress In Materials Science Research
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Author : Antonio C. Venetti
language : en
Publisher: Nova Publishers
Release Date : 2008
Progress In Materials Science Research written by Antonio C. Venetti and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.