This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend.

Author: L.D. Faddeev

Publisher: Springer Science & Business Media

ISBN: 0792324145

Category: Science

Page: 430

View: 890

The last decade witnessed an increasing interest of mathematicians in prob lems originated in mathematical physics. As a result of this effort, the scope of traditional mathematical physics changed considerably. New problems es pecially those connected with quantum physics make use of new ideas and methods. Together with classical and functional analysis, methods from dif ferential geometry and Lie algebras, the theory of group representation, and even topology and algebraic geometry became efficient tools of mathematical physics. On the other hand, the problems tackled in mathematical physics helped to formulate new, purely mathematical, theorems. This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend. In our view, however, an adequate language and appropriate methodology has not been developed yet. Nowadays, the current literature includes either mathematical monographs occasionally using physical terms, or books on theoretical physics focused on the mathematical apparatus. We hold the opinion that the traditional mathematical language of lem mas and theorems is not appropriate for the contemporary writing on mathe matical physics. In such literature, in contrast to the standard approaches of theoretical physics, the mathematical ideology must be utmost emphasized and the reference to physical ideas must be supported by appropriate mathe matical statements. Of special importance are the results and methods that have been developed in this way for the first time.

For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding.

Author: Jan Derezinski

Publisher: Springer Science & Business Media

ISBN: 3540620664

Category: Science

Page: 468

View: 671

This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.

52 2.3.2 The scattering operator . ... 56 2.4 Singularities of Resolvent for Charged Particles . . . . . . . . 57 2.4.1 Resolvent and wave operators . ... 62 3.2 Compact Integral Equations for Three-Particle Systems .

Author: L.D. Faddeev

Publisher: Springer Science & Business Media

ISBN: 9789401728324

Category: Science

Page: 406

View: 398

The last decade witnessed an increasing interest of mathematicians in prob lems originated in mathematical physics. As a result of this effort, the scope of traditional mathematical physics changed considerably. New problems es pecially those connected with quantum physics make use of new ideas and methods. Together with classical and functional analysis, methods from dif ferential geometry and Lie algebras, the theory of group representation, and even topology and algebraic geometry became efficient tools of mathematical physics. On the other hand, the problems tackled in mathematical physics helped to formulate new, purely mathematical, theorems. This important development must obviously influence the contemporary mathematical literature, especially the review articles and monographs. A considerable number of books and articles appeared, reflecting to some extend this trend. In our view, however, an adequate language and appropriate methodology has not been developed yet. Nowadays, the current literature includes either mathematical monographs occasionally using physical terms, or books on theoretical physics focused on the mathematical apparatus. We hold the opinion that the traditional mathematical language of lem mas and theorems is not appropriate for the contemporary writing on mathe matical physics. In such literature, in contrast to the standard approaches of theoretical physics, the mathematical ideology must be utmost emphasized and the reference to physical ideas must be supported by appropriate mathe matical statements. Of special importance are the results and methods that have been developed in this way for the first time.

Self-contained treatment of nonrelativistic many-particle systems discusses both formalism and applications in terms of ground-state (zero-temperature) formalism, finite-temperature formalism, canonical transformations, and applications to ...

Author: Alexander L. Fetter

Publisher: Courier Corporation

ISBN: 9780486134758

Category: Science

Page: 640

View: 595

Self-contained treatment of nonrelativistic many-particle systems discusses both formalism and applications in terms of ground-state (zero-temperature) formalism, finite-temperature formalism, canonical transformations, and applications to physical systems. 1971 edition.

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 ...

Author: Dzevad Belkic

Publisher: CRC Press

ISBN: 1420033646

Category: Science

Page: 402

View: 219

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.

Sophisticated N-Particle Scattering in Quantum Mechanics L. Faddeev and S. Merkuryev, Quantum Scattering Theory for Several Particle Systems, Kluwer, Dordrecht, 1996. (In 1963 Faddeev solved the quantum three-body problem.) ...

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 9783540853770

Category: Mathematics

Page: 1101

View: 826

And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don’t give us numbers: give us insight! A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravitation and String Theory. It is our goal to build a bridge between mathematicians and physicists based on the challenging question about the fundamental forces in • macrocosmos (the universe) and • microcosmos (the world of elementary particles). The six volumes address a broad audience of readers, including both und- graduate and graduate students, as well as experienced scientists who want to become familiar with quantum ?eld theory, which is a fascinating topic in modern mathematics and physics.

In a certain way it is the opposite of the book of Reed and Simon: a physics book with great attention for the mathematical background.) 4. Faddeev, L.D., Merkuriev, S.P.: Quantum Scattering Theory for Several Particle Systems.

Author: Peter Bongaarts

Publisher: Springer

ISBN: 9783319095615

Category: Science

Page: 445

View: 653

This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

Faddeev, L.D., and Merkuriev, S.P., Quantum Scattering Theory for Several Particle Systems, Kluwer Academic Publishers, Dordrecht, 1993. [H.M. Stationary Office, Harwell, 1964]. [55] Jauch, J.M., On the relation between scattering phase ...

Author: Dzevad Belkic

Publisher: CRC Press

ISBN: 158488729X

Category: Science

Page: 432

View: 321

One of the Top Selling Physics Books according to YBP Library Services Suitable for graduate students, experienced researchers, and experts, this book provides a state-of-the-art review of the non-relativistic theory of high-energy ion-atom collisions. Special attention is paid to four-body interactive dynamics through the most important theoretical methods available to date by critically analyzing their foundation and practical usefulness relative to virtually all the relevant experimental data. Fast ion-atom collisions are of paramount importance in many high-priority branches of science and technology, including accelerator-based physics, the search for new sources of energy, controlled thermonuclear fusion, plasma research, the earth’s environment, space research, particle transport physics, therapy of cancer patients by heavy ions, and more. These interdisciplinary fields are in need of knowledge about many cross sections and collisional rates for the analyzed fast ion-atom collisions, such as single ionization, excitation, charge exchange, and various combinations thereof. These include two-electron transitions, such as double ionization, excitation, or capture, as well as simultaneous electron transfer and ionization or excitation and the like—all of which are analyzed in depth in this book. Quantum Theory of High-Energy Ion-Atom Collisions focuses on multifaceted mechanisms of collisional phenomena with heavy ions and atoms at non-relativistic high energies.

An analogous system of N quantum particles is described by a Hamiltonian of the form N- 1 H. := — XD 3:44 + XD ... In fact, in many experiments the particles are initially far apart, then they scatter from one another and at the end ...

Author: Jan Derezinski

Publisher: Springer Science & Business Media

ISBN: 9783662034033

Category: Science

Page: 444

View: 879

This monograph addresses researchers and students. It is a modern presentation of time-dependent methods for studying problems of scattering theory in the classical and quantum mechanics of N-particle systems. Particular attention is paid to long-range potentials. For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown. The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N-body Hamiltonians) is presented with deep insight into the physical and mathematical problems.

[15] L.D. Faddeev and S.P. Merkuriev, Quantum Scattering Theory For Several Particle Systems. Kluwer, Dorolrect, 1993. [16] D.G. Truhlar and B. Simon, Multi-Particle Quantum Scattering with Applications to Nuclear, Atomic and Molecular ...

Author: S. Rajasekar

Publisher: CRC Press

ISBN: 9781000729030

Category: Science

Page: 803

View: 763

Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems. This fully updated new edition addresses many topics not typically found in books at this level, including: Bound state solutions of quantum pendulum Morse oscillator Solutions of classical counterpart of quantum mechanical systems A criterion for bound state Scattering from a locally periodic potential and reflection-less potential Modified Heisenberg relation Wave packet revival and its dynamics An asymptotic method for slowly varying potentials Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell’s theorem Delayed-choice experiments Fractional quantum mechanics Numerical methods for quantum systems A collection of problems at the end of each chapter develops students’ understanding of both basic concepts and the application of theory to various physically important systems. This book, along with the authors’ follow-up Quantum Mechanics II: Advanced Topics, provides students with a broad, up-to-date introduction to quantum mechanics. Print Versions of this book also include access to the ebook version.