This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba tion terms with singular properties. Typical examples of such expressions are Schrodin ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(
BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical PhysicsThis revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.
This book presents a comprehensive account of molecular quantum electrodynamics from the perspectives of physics and theoretical chemistry. The first part of the book establishes the essential concepts underlying classical electrodynamics, using the tools of Lagrangian and Hamiltonian mechanics. The second part focuses on the fundamentals of quantum mechanics, particularly how they relate to, and influence, chemical and molecular processes. The special case of the Coulomb Hamiltonian (including the celebrated Born-Oppenheimer approximation) is given a modern treatment. The final part of the book is devoted to non-relativistic quantum electrodynamics and describes in detail its impact upon our understanding of atoms and molecules, and their interaction with light. Particular attention is paid to the Power-Zienau-Woolley (PZW) representations, and both perturbative and non-perturbative approaches to QED calculation are discussed. This book is ideal for graduate students and researchers in chemical and molecular physics, quantum chemistry, and theoretical chemistry.
"Imagination and shrewd guesswork are powerful instruments for acquiring scientific knowledge . . . " 1. H. van't Hoff The last decades have witnessed a rapid growth of quantum chemistry and a tremendous increase in the number of very accurate ab initio calculations of the electronic structure of molecules yielding results of admirable accuracy. This dramatic progress has opened a new stage in the quantum mechanical description of matter at the molecular level. In the first place, highly accurate results provide severe tests of the quantum mecha nics. Secondly, modern quantitative computational ab initio methods can be synergetically combined with various experimen tal techniques thus enabling precise numerical characterization of molecular properties better than ever anticipated earlier. However, the role of theory is not exhausted in disclosing the fundamental laws of Nature and production of ever increasing sets of data of high accuracy. It has to provide additionally a means of systematization, recognition of regularities, and ratio nalization of the myriads of established facts avoiding in this way complete chaos. Additional problems are represented by molecular wavefunctions provided by the modern high-level computational quantum chemistry methods. They involve, in principle, all the information on molecular system, but they are so immensely complex that can not be immediately understood in simple and physically meaningful terms. Both of these aspects, categorization and interpretation, call for conceptual models which should be preferably pictorial, transparent, intuitively appealing and well-founded, being sometimes useful for semi quantitative purposes.
Stochastic mechanics is a description of quantum phenomena in classical probabilistic terms. This work contains a detailed account of the kinematics of diffusion processes, including diffusions on curved manifolds which are necessary for the treatment of spin in stochastic mechanics. The dynamical equations of the theory are derived from a variational principle, and interference, the asymptotics of free motion, bound states, statistics, and spin are described in classical terms. In addition to developing the formal mathematical aspects of the theory, the book contains discussion of possible physical causes of quantum fluctuations in terms of an interaction with a background field. The author gives a critical analysis of stochastic mechanics as a candidate for a realistic theory of physical processes, discussing measurement, local causality in the sense of Bell, and the failure of the theory in its present form to satisfy locality.
From a review of the first edition: Beautifully written and well organized ... indispensable for those interested in certain areas of mathematical physics ... for the expert and beginner alike. The author deserves to be congratulated both for his work in unifying a subject and for showing workers in the field new directions for future development. --Zentralblatt MATH This is a second edition of a well-known book on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this second edition, the author has added four chapters on the closely related theory of rank one perturbations of self-adjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published. This book continues to be a vital source of information for those interested in the theory of trace ideals and in its applications to various areas of mathematical physics.
