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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.
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.
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.
For more than a century, studies of atomic hydrogen have been a rich source of scientific discoveries. These began with the Balmer series in 1885 and the early quantum theories of the atom, and later included the development of QED and the first successful gauge field theory. Today, hydrogen and its relatives continue to provide new fundamental information, as witnessed by the contributions to this book. The printed volume contains invited reviews on the spectroscopy of hydrogen, muonium, positronium, few-electron ions and exotic atoms, together with related topics such as frequency metrology and the determination of fundamental constants. The accompanying CD contains, in addition to these reviews, a further 40 contributed papers also presented at the conference "Hydrogen Atom 2" held in summer 2000. Finally, to facilitate a historical comparison, the CD also contains the proceedings of the first "Hydrogen Atom" conference of 1988. The book includes a foreword by Norman F. Ramsey.
Written by two researchers in the field, this book is a reference to explain the principles and fundamentals in a self-contained, complete and consistent way. Much attention is paid to the didactical value, with the chapters interconnected and based on each other. From the contents: * Fundamentals * Relativistic Theory of a Free Electron: Diracï¿1⁄2s Equation * Dirac Theory of a Single Electron in a Central Potential * Many-Electron Theory I: Quantum Electrodynamics * Many-Electron Theory II: Dirac-Hartree-Fock Theory * Elimination of the Small Component * Unitary Transformation Schemes * Relativistic Density Functional Theory * Physical Observables and Molecular Properties * Interpretive Approach to Relativistic Quantum Chemistry From beginning to end, the authors deduce all the concepts and rules, such that readers are able to understand the fundamentals and principles behind the theory. Essential reading for theoretical chemists and physicists.
To honour W C Röntgen and review the entire area of X-ray development in the various fields of natural, technical, and life sciences, his successors at the Physikalisches Institut of the Universität Würzburg organized a conference, named “Röntgen Centennial”. It took place at the new “Physikalisches Institut” not far from the historical site shortly before the actual 100th anniversary of the discovery. Over forty renowned scientists were invited as representative speakers in the various subfields of X-ray activities. They reviewed the development, gave examples, and described the present status. Most of them provided survey articles, which are gathered in this book. Since most X-ray-related activities are somehow represented, an almost complete overview of the entire field is provided. This book thus represents the enormous breadth of X-ray activities and allows one to recognize the potential and quality of today's X-ray research.
The physics of atomic inner shells has undergone significant advances in recent years. Fast computers and new experimental tools, notably syn chrotron-radiation sources and heavy-ion accelerators, have greatly enhan ced the scope of problems that are accessible. The level of research activity is growing substantially; added incentives are provided by the importance of inner-shell processes in such diverse areas as plasma studies, astrophysics, laser technology, biology, medicine, and materials science. The main reason for all this exciting activity in atomic inner-shell physics, to be sure, lies in the significance of the fundamental problems that are coming within grasp. The large energies of many inner-shell processes cause relativistic and quantum-electrodynamic effects to become strong. Unique opportunities exist for delicate tests of such phenomena as the screening of the electron self-energy and the limits of validity of the present form of the frequency-dependent Breit interaction, to name but two. The many-body problem, which pervades virtually all of physics, presents somewhat less intractable aspects in the atomic inner-shell regime: correlations are relatively weak so that they can be treated perturbatively, and the basic potential is simple and known! The dynamics of inner-shell processes are characterized by exceedingly short lifetimes and high transition rates that strain perturbation theory to its limits and obliterate the traditional separation of excitation and deexcitation. These factors are only now being explored, as are interference phenomena between the various channels.