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Author: G. Velo
Publisher: Springer Science & Business Media
ISBN: 1461333504
Category : Science
Languages : en
Pages : 498
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Book Description
One of the goals of mathematical physics is to provide a rigorous derivation of the properties of macroscopic matter starting from Schrodinger's equation. Although at the present time this objective is far from being realized, there has been striking recent progress, and the fourth "Ettore Majorana" International School of Mathematical Physics held at Erice, 1-15 June 1980 with the title Rigorous Atomic and Mqlecular Physics focussed on some of the recent advances. The first of these is the geometric method in the theory of scattering. Quantum mechanical scattering theory is an old and highly cultivated subject, but, until recently, many of its fundamental developments were technically very complicated and conceptually rather obscure. For example, one of the basic properties of a system of N particles moving under the influence of appropriately restricted short-range plus Coulomb forces is asymptotic completeness: the space of states is spanned by the bound states and scattering states. However, the proof of asymp totic. completeness for N bodies was achieved only with physically unsatisfactory restrictions on the nature of the interaction and even for N = 2 required an involved argument rather more subtle than the physical circumstances seemed to warrant. The reader will find in the present volume a very simple and physical proof of asymptotic completeness for N = 2 as well as an outline of the geometrical ideas which are currently being used to attack the problem for N > 2. (See the lectures of Enss.
Author: G. Velo
Publisher: Springer Science & Business Media
ISBN: 1461333504
Category : Science
Languages : en
Pages : 498
Get Book Here
Book Description
One of the goals of mathematical physics is to provide a rigorous derivation of the properties of macroscopic matter starting from Schrodinger's equation. Although at the present time this objective is far from being realized, there has been striking recent progress, and the fourth "Ettore Majorana" International School of Mathematical Physics held at Erice, 1-15 June 1980 with the title Rigorous Atomic and Mqlecular Physics focussed on some of the recent advances. The first of these is the geometric method in the theory of scattering. Quantum mechanical scattering theory is an old and highly cultivated subject, but, until recently, many of its fundamental developments were technically very complicated and conceptually rather obscure. For example, one of the basic properties of a system of N particles moving under the influence of appropriately restricted short-range plus Coulomb forces is asymptotic completeness: the space of states is spanned by the bound states and scattering states. However, the proof of asymp totic. completeness for N bodies was achieved only with physically unsatisfactory restrictions on the nature of the interaction and even for N = 2 required an involved argument rather more subtle than the physical circumstances seemed to warrant. The reader will find in the present volume a very simple and physical proof of asymptotic completeness for N = 2 as well as an outline of the geometrical ideas which are currently being used to attack the problem for N > 2. (See the lectures of Enss.
Author: G Velo
Publisher:
ISBN: 9781461333517
Category :
Languages : en
Pages : 510
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Book Description
Author: Sakir Erkoc
Publisher: World Scientific
ISBN: 9814498394
Category : Science
Languages : en
Pages : 322
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Book Description
This book aims to present a unified account of the physics of atoms and molecules from a modern viewpoint. It is based on courses given by the authors at Middle East Technical University, Ankara and Georgia Institute of Technology, Atlanta, and is suitable for study at third and fourth year levels of an undergraduate course.Students should be able to read this volume and understand its contents without the need to supplement it by referring to more detailed discussions. The whole subject covered in this volume is expected to be finished in one semester.
Author: William McClain
Publisher: Springer Science & Business Media
ISBN: 0387734708
Category : Science
Languages : en
Pages : 672
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Book Description
Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.
Author: Dzevad Belkic
Publisher: CRC Press
ISBN: 9781420033649
Category : Science
Languages : en
Pages : 402
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Book Description
Scattering is one of the most powerful methods used to study the structure of matter, and many of the most important breakthroughs in physics have been made by means of scattering. Nearly a century has passed since the first investigations in this field, and the work undertaken since then has resulted in a rich literature encompassing both experimental and theoretical results. In scattering, one customarily studies collisions among nuclear, sub-nuclear, atomic or molecular particles, and as these are intrinsically quantum systems, it is logical that quantum mechanics is used as the basis for modern scattering theory. In Principles of Quantum Scattering Theory, the author judiciously combines physical intuition and mathematical rigour to present various selected principles of quantum scattering theory. As always in physics, experiment should be used to ultimately validate physical and mathematical modelling, and the author presents a number of exemplary illustrations, comparing theoretical and experimental cross sections in a selection of major inelastic ion-atom collisions at high non-relativistic energies. Quantum scattering theory, one of the most beautiful theories in physics, is also very rich in mathematics. Principles of Quantum Scattering Theory is intended primarily for graduate physics students, but also for non-specialist physicists for whom the clarity of exposition should aid comprehension of these mathematical complexities.
Author: Charles E. Burkhardt
Publisher: Springer Science & Business Media
ISBN: 0387310746
Category : Science
Languages : en
Pages : 298
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Book Description
The importance of the ?eld of atomic physics to modern technology cannot be overemphasized. Atomic physics served as a major impetus to the development of the quantum theory of matter in the early part of the twentieth century and, due to the availability of the laser as a laboratory tool, it has taken us into the twen- ?rst century with an abundance of new and exciting phenomena to understand. Our intention in writing this book is to provide a foundation for students to begin researchinmodernatomicphysics. Asthetitleimplies,itisnot,norwasitintended to be, an all-inclusive tome covering every aspect of atomic physics. Any specialized textbook necessarily re?ects the predilection of the authors toward certain aspects of the subject. This one is no exception. It re?ects our - lief that a thorough understanding of the unique properties of the hydrogen atom is essential to an understanding of atomic physics. It also re?ects our fasci- tion with the distinguished position that Mother Nature has bestowed on the pure Coulomb and Newtonian potentials, and thus hydrogen atoms and Keplerian - bits. Therefore, we have devoted a large portion of this book to the hydrogen atom toemphasizethisdistinctiveness. Weattempttostresstheuniquenessoftheattr- tive 1/r potential without delving into group theory. It is our belief that, once an understanding of the hydrogen atom is achieved, the properties of multielectron atoms can be understood as departures from hydrogenic properties.
Author: Mitchel Weissbluth
Publisher: Elsevier
ISBN: 032314294X
Category : Science
Languages : en
Pages : 730
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Book Description
Atoms and Molecules describes the basic properties of atoms and molecules in terms of group theoretical methods in atomic and molecular physics. The book reviews mathematical concepts related to angular momentum properties, finite and continuous rotation groups, tensor operators, the Wigner-Eckart theorem, vector fields, and vector spherical harmonics. The text also explains quantum mechanics, including symmetry considerations, second quantization, density matrices, time-dependent, and time-independent approximation methods. The book explains atomic structure, particularly the Dirac equation in which its nonrelativistic approximation provides the basis for the derivation of the Hamiltonians for all important interactions, such as spin-orbit, external fields, hyperfine. Along with multielectron atoms, the text discusses multiplet theory, the Hartree-Fock formulation, as well as the electromagnetic radiation fields, their interactions with atoms in first and higher orders. The book explores molecules and complexes, including the Born-Oppenheimer approximation, molecular orbitals, the self-consistent field method, electronic states, vibrational and rotational states, molecular spectra, and the ligand field theory. The book can prove useful for graduate or advanced students and academicians in the field of general and applied physics.
Author: Franco A. Gianturco
Publisher: Springer Science & Business Media
ISBN: 1461333121
Category : Science
Languages : en
Pages : 508
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Book Description
Until recently, the field of atomic and molecular collisions was left to a handful of practitioners who essentially explored it as a branch of atomic physics and gathered their experimental re sults mainly from spectroscopy measurements in bulk. But in the past ten years or so, all of this has dramatically changed, and we are now witnessing the rapid growth of a large body of research that encompasses the simplest atoms as well as the largest mole cules, that looks at a wide variety of phenomena well outside purely spectroscopic observation, and that finds applications in an unexpectedly broad range of physico-chemical and physical pro cesses. The latter are in turn surprisingly close to very important sectors of applied research, such as the modeling of molecular lasers, the study of isotope separation techniques, and the energy losses in confined plasmas, to mention just a few of them. As a consequence of this healthy state of affairs, greatly diversified research pathways have developed; however, their specialized problems are increasingly at risk of being viewed in isolation, although they are part of a major and extended branch of physics or chemistry. This is particularly true when it comes to the theory of this work -- where well-established methods and models of one subfield are practically unknown to researchers in other subfields -- and, consequently, the danger of wasteful duplication arising is quite real.
Author: Luciano Colombo
Publisher:
ISBN: 9780750322607
Category : Nuclear physics
Languages : en
Pages : 0
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Book Description
"This book introduces the fundamental quantum physics of atoms and molecules. Divided into three parts, the first provides a historical perspective leading to the contemporary view of atomic and molecular physics, outlining the principles of non-relativistic quantum mechanics. The second part covers the physical description of atoms and their interaction with radiation, whilst the third part deals with molecular physics." -- Prové de l'editor.
Author: Elliott H. Lieb
Publisher: Springer Science & Business Media
ISBN: 3662027259
Category : Science
Languages : en
Pages : 565
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Book Description
With this book, Elliott Lieb joins his peers Hermann Weyl and Chen Ning Yang. Weyl's Selecta was published in 1956, Yang's Selected Papers in 1983. Lieb's "Selecta", like its predecessors, gives us the essence of a great mathema tical physicist concentrated into one convenient volume. Weyl, Yang and Lieb have much more in common than the accident of this manner of publication. They have in common a style and a tradition. Each of them is master of a for midable mathematical technique. Each of them uses hard mathematical ana lysis to reach an understanding of physical laws. Each of them enriches both physics and mathematics by finding new mathematical depths in the description of familiar physical processes. The central theme of Weyl's work in mathematical physics was the idea of symmetry, linking physical invariance-principles with the mathematics of group-theory. One of Yang's central themes is the idea of a gauge field, linking physical interactions with the mathematics of fibre-bundles. The central theme of Lieb's papers collected in this book is the classical Thomas-Fermi model of an atom, linking the physical stability of matter with the mathematics of func tional analysis. In all three cases, a rather simple physical idea provided the starting-point for building a grand and beautiful mathematical structure. Weyl, Yang and Lieb were not content with merely solving a problem. Each of them was concerned with understanding the deep mathematical roots out of which physical phenomena grow.
