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Author: Roger Boudet Publisher: Springer Science & Business Media ISBN: 3540855505 Category : Science Languages : en Pages : 127
Book Description
The aim of this volume is twofold. First, it is an attempt to simplify and clarify the relativistic theory of the hydrogen-like atoms. For this purpose we have used the mathematical formalism, introduced in the Dirac theory of the electron by David Hestenes, based on the use of the real Cli?ord algebra Cl(M) associated with the Minkwoski space–time M, that is, the euclidean 4 R space of signature (1,3). This algebra may be considered as the extension to this space of the theory of the Hamilton quaternions (which occupies an importantplaceintheresolutionoftheDiracequationforthecentralpotential problem). The clarity comes from the real form given by D. Hestenes to the electron wavefunctionthatreplaces,inastrictequivalence,theDiracspinor.Thisform is directly inscribed in the frame of the geometry of the Minkwoski space in which the experiments are necessarily placed. The simplicity derives from the uni?cation of the language used to describe the mathematical objects of the theory and the data of the experiments. The mathematics concerning the de?nition and the use of the algebra Cl(M) are not very complicated. Anyone who knows what a vector space is will be able to understand the geometrical implications of this algebra. The lecture will be perhaps more di?cult for the readers already acquainted with the complex formalism of the matrices and spinors, to the extent that the new language will appear di?erent from the one that they have used. But the correspondence between the two formalisms is ensured in the text at each stage of the theory.
Author: Roger Boudet Publisher: Springer Science & Business Media ISBN: 3540855505 Category : Science Languages : en Pages : 127
Book Description
The aim of this volume is twofold. First, it is an attempt to simplify and clarify the relativistic theory of the hydrogen-like atoms. For this purpose we have used the mathematical formalism, introduced in the Dirac theory of the electron by David Hestenes, based on the use of the real Cli?ord algebra Cl(M) associated with the Minkwoski space–time M, that is, the euclidean 4 R space of signature (1,3). This algebra may be considered as the extension to this space of the theory of the Hamilton quaternions (which occupies an importantplaceintheresolutionoftheDiracequationforthecentralpotential problem). The clarity comes from the real form given by D. Hestenes to the electron wavefunctionthatreplaces,inastrictequivalence,theDiracspinor.Thisform is directly inscribed in the frame of the geometry of the Minkwoski space in which the experiments are necessarily placed. The simplicity derives from the uni?cation of the language used to describe the mathematical objects of the theory and the data of the experiments. The mathematics concerning the de?nition and the use of the algebra Cl(M) are not very complicated. Anyone who knows what a vector space is will be able to understand the geometrical implications of this algebra. The lecture will be perhaps more di?cult for the readers already acquainted with the complex formalism of the matrices and spinors, to the extent that the new language will appear di?erent from the one that they have used. But the correspondence between the two formalisms is ensured in the text at each stage of the theory.
Author: Alexander Voitkiv Publisher: Springer Science & Business Media ISBN: 3540784217 Category : Science Languages : en Pages : 289
Book Description
During the last two decades the explorations of di?erent processes accom- nyingion–atom collisions athigh-impactenergieshavebeenasubjectofmuch interest. This interest was generated not only by the advent of accelerators of relativistic heavy ions which enabled one to investigate these collisions in an experiment and possible applications of obtained results in other ?elds of physics, but also by the variety of physical mechanisms underlying the atomic collisional phenomena at high impact energies. Often highly charged projectiles produced at accelerators of heavy ions are not fully stripped ions but carry one or more very tightly bound el- trons. In collisions with atomic targets, these electrons can be excited or lost and this may occur simultaneously with electronic transitions in the target. The present book concentrates on, and may serve as an introduction to, th- retical methods which are used to describe the projectile–electron transitions occurringinhigh-energycollisionsbetweenionsandneutralatoms.Special- tention is given to relativistic impact energies and highly charged projectiles. Experimental results are used merely as illustrations and tests for theory. This book will be useful to graduate students and professional scientists who are interested in studying atomic collisions occurring at high-impact - ergies. It assumes that the reader possesses the basic knowledge in classical electrodynamics and nonrelativistic and relativistic quantum mechanics.
Author: Ian P Grant Publisher: Springer Science & Business Media ISBN: 0387350691 Category : Science Languages : en Pages : 813
Book Description
This book is intended for physicists and chemists who need to understand the theory of atomic and molecular structure and processes, and who wish to apply the theory to practical problems. As far as practicable, the book provides a self-contained account of the theory of relativistic atomic and molecular structure, based on the accepted formalism of bound-state Quantum Electrodynamics. The author was elected a Fellow of the Royal Society of London in 1992.
Author: G.L. Malli Publisher: Springer Science & Business Media ISBN: 1461335965 Category : Science Languages : en Pages : 539
Book Description
The NATO Advanced Study Institute (ASI) on "Relativistic Effects in Atoms, Molecules and Solids" cosponsored by Simon Fraser University (SFU) and Natural Sciences and Engineering Research Council of Canada (NSERC) was held at the University of British Columbia (UBC) , Van couver, Canada from August 10th until August 21st, 1981. A total of 77 lecturers and students with diverse backgrounds in Chemistry, Physics, Mathematics and various interdisciplinary subjects attended the ASI. In the proposal submitted to NATO for financial support for this ASI, it was suggested that recent impressive experimental developments coupled with the availability of sophisticated computer technology for detailed investigation of the relativistic structure of atoms, molecules and solids would provide an excellent testing ground for the validity and accuracy of the theoretical treatment of the rela tivistic many-electron systems involving medium and heavy atoms. Such systems are also of interest to the current energy crisis because of their usage for photovoltaic devices, nuclear fuels (UF6), fusion lasers (Xe*2)' catalysts for solar energy conversion, etc.
Author: Igor I. Sobelman Publisher: Springer Science & Business Media ISBN: 3642769071 Category : Science Languages : en Pages : 367
Book Description
Atomic Spectra and Radiative Transitions covers the systematics of atomic spectra, continuous spectrum radiation, and the excitation of atoms. This second edition has additional chapters on relativistic corrections in the spectra of highly charged ions, which rounds off the previous treatment. Extensive tables of oscillator strengths (both dipole and quadrupole), probabilities and cross sections of radiative transitions complete this textbook, making it invaluable also as a reference work.
Author: OpenStax Publisher: ISBN: 9781680920451 Category : Science Languages : en Pages : 622
Book Description
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale.
Author: Kenneth G. Dyall Publisher: Oxford University Press ISBN: 0190286377 Category : Science Languages : en Pages : 544
Book Description
This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.
Author: Roger Boudet
Author: Roger Boudet
Author: Alain Amand Gautier
Author: Alexander Voitkiv
Author: Pekka Pyykkö
Author: Ian P Grant
Author: Jen-hsiung Tung
Author: G.L. Malli
Author: Igor I. Sobelman
Author: OpenStax
Author: Kenneth G. Dyall