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KAM Theory and Semiclassical Approximations to Eigenfunctions, Vladimir F. Lazutkin; A.I. Shnirelman


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Автор: Vladimir F. Lazutkin; A.I. Shnirelman
Название:  KAM Theory and Semiclassical Approximations to Eigenfunctions
ISBN: 9783642762499
Издательство: Springer
Классификация: ISBN-10: 3642762492
Обложка/Формат: Paperback
Страницы: 387
Вес: 0.63 кг.
Дата издания: 14.12.2011
Серия: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Язык: English
Размер: 244 x 170 x 21
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: It is a surprising fact that so far almost no books have been published on KAM theory. The first part of this book seems to be the first monographic exposition of this subject, despite the fact that the discussion of KAM theory started as early as 1954 (Kolmogorov) and was developed later in 1962 by Arnold and Moser. Today, this mathematical field is very popular and well known among physicists and mathematicians. In the first part of this Ergebnisse-Bericht, Lazutkin succeeds in giving a complete and self-contained exposition of the subject, including a part on Hamiltonian dynamics. The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory. The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schr dinger operator. The main result is the asymptotic formulae for eigenfunctions and eigenvalues, using Maslov s operator, for the set of eigenvalues of positive density in the set of all eigenvalues. An addendum by Prof. A.I. Shnirelman treats eigenfunctions corresponding to the chaotic component of the phase space.

Semiclassical Theory of Atoms

Автор: Berthold-G. Englert
Название: Semiclassical Theory of Atoms
ISBN: 3662136813 ISBN-13(EAN): 9783662136812
Издательство: Springer
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Semiclassical Theory of Mesoscopic Quantum Systems

Автор: Klaus Richter
Название: Semiclassical Theory of Mesoscopic Quantum Systems
ISBN: 3662156504 ISBN-13(EAN): 9783662156506
Издательство: Springer
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Цена: 46570.00 T
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Описание: This book describes manifestations of classical dynamics and chaos in the quantum properties of mesoscopic systems.

Semiclassical Dynamics and Relaxation

Автор: D.S.F. Crothers
Название: Semiclassical Dynamics and Relaxation
ISBN: 1441925546 ISBN-13(EAN): 9781441925541
Издательство: Springer
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Цена: 130590.00 T
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Описание: Physicists will find this text useful. It is a rigorous and comprehensive discussion of the mathematics of semiclassical theory to condensed-matter physics. The author has 42 years` experience in quantum dynamics and the processes of atomic collisions.

Functional Integration and Semiclassical Expansions

Автор: Flor Langouche; Dirk Roekaerts; E. Tirapegui
Название: Functional Integration and Semiclassical Expansions
ISBN: 9048183774 ISBN-13(EAN): 9789048183777
Издательство: Springer
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Цена: 130430.00 T
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Описание: This book is intended as a fairly complete presentation of what--'We call the discretization approach to functional integrals, i.e. path integrals defined as limits of discretized axpressions. In its main parts it is based 0n the original work of the authors. We hope to have provided the readers with a rather complete and up-to-date bibliography, and we apologize to authors whose work has not been cited through ignorance ori our part. Our main concern has been to present a for- malism that is practical and which can be adapted to make computations in the numerous areas where path integrals are being increasingly used. For these reasons applications, illustrative examples, and detailed calculations are included. The book is partially based on lectures given by one of us (E.T.) at the Institut de Physique Theorique of the u.c.L. (Louvain-la-Neuve). We thank Dr. M.E. Brachet (University of Paris) for his help in the redaction of chapter 8. We are indebted to many of our colleagues and especially to the members of the Instituut voor Theoretische Fysica, K.U. Leuven for their interest and encouragement. We also thank Professor Claudio Anguita, Dean of the Faculty of Physics and Mathematics of .the University of Chile, for his constant support. Special thanks are due to Christine Detroije and Lutgarde Dubois for their very fine and hard work in typing the manuscript.

Semiclassical Methods in Molecular Scattering and Spectroscopy

Автор: M.S. Child
Название: Semiclassical Methods in Molecular Scattering and Spectroscopy
ISBN: 9400989989 ISBN-13(EAN): 9789400989986
Издательство: Springer
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Цена: 111790.00 T
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Описание: Proceedings of the NATO Advanced Study Institute, Cambridge, England, September 1979

Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. (MN-29)

Автор: Agmon Shmuel
Название: Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. (MN-29)
ISBN: 0691613672 ISBN-13(EAN): 9780691613673
Издательство: Wiley
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Цена: 31680.00 T
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Описание: Mathematical Notes, 29 Originally published in 1983. 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 paper

An Introduction to Semiclassical and Microlocal Analysis

Автор: Andr? Bach
Название: An Introduction to Semiclassical and Microlocal Analysis
ISBN: 1441929614 ISBN-13(EAN): 9781441929617
Издательство: Springer
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Описание: The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are mainly addressed to nonspecialists in the subject, and their purpose is to present in a pedagogical way most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard Coo pseudodifferential calculus and the analytic microlocal analysis are developed, in a context that remains intentionally global so that only the relevant difficulties of the theory are encountered. The main original- ity lies in the fact that we derive all the main features of analytic microlocal analysis from a single a priori estimate, which turns out to be elementary once the Coo pseudodifferential calculus is established. Various detailed exercises are given at the end of the main chapters, most of them being easily solvable by students. Besides illustrating the main results of the lecture, their aim is also to introduce the reader to various further developments of the theory, such as the functional calculus of pseudodifferential operators, properties of the analytic wave front set, Gevrey classes, the use of coherent states, the notion of semiclassical measures, WKB constructions. Applications to the study of the Schrodinger operator are also discussed in the text, so that they may help the understanding of new notions or general results where they appear by replacing them in the context of quantum mechanics.

Classical, Semiclassical and Quantum Dynamics in Atoms

Автор: Harald Friedrich; Bruno Eckhardt
Название: Classical, Semiclassical and Quantum Dynamics in Atoms
ISBN: 3662141523 ISBN-13(EAN): 9783662141526
Издательство: Springer
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Molecular Symmetry, Super-Rotation, and Semiclassical Motion

Автор: Hanno Schmiedt
Название: Molecular Symmetry, Super-Rotation, and Semiclassical Motion
ISBN: 3319660705 ISBN-13(EAN): 9783319660707
Издательство: Springer
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Цена: 93160.00 T
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Описание:

New ideas to old problems - An introduction

Part I Group theory in molecular physics

1 Basic concepts

2 Schur-Weyl duality in molecules

3 Reactive collisions

Part II Extremely floppy molecules

1 Introducing extreme floppiness

2 Symmetry beyond perturbation theory

3 The molecular super-rotor

4 Super-rotor states and their symmetry

5 Protonated methane

6 Refinements and further applications

Part III Semi-classical approach to rotational dynamics

1 Ultrafast rotation

2 Application to sulfur dioxide

3 Discussion

New ideas to old problems - A conclusion


Semiclassical Methods in Molecular Scattering and Spectroscopy

Автор: M.S. Child
Название: Semiclassical Methods in Molecular Scattering and Spectroscopy
ISBN: 9027710821 ISBN-13(EAN): 9789027710826
Издательство: Springer
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Цена: 177010.00 T
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Описание: Proceedings of the NATO Advanced Study Institute, Cambridge, England, September 1979

Semiclassical Theories of Molecular Scattering

Автор: B. C. Eu
Название: Semiclassical Theories of Molecular Scattering
ISBN: 364288167X ISBN-13(EAN): 9783642881671
Издательство: Springer
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Цена: 46570.00 T
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Описание: The study of molecular collisions at energies from less than about 100 eV 3 down to a few 10- eV, which is roughly the range of chemical interest, has greatly expanded in the last 10 to 20 years.


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