Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

The book provides a general, broad approach to aspects of perturbation theory.

Author: Gustavo A. Arteca

Publisher: Springer Science & Business Media

ISBN: 9783642934698

Category: Science

Page: 644

View: 158

The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.
Categories: Science

Large Order Behaviour of Perturbation Theory

Large Order Behaviour of Perturbation Theory

This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series.

Author: J.C. Le Guillou

Publisher: Elsevier

ISBN: 9780444596208

Category: Science

Page: 595

View: 109

This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series. Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small. The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of &fgr;4 field theory is presented as a practical application.
Categories: Science

Introduction to Perturbation Theory in Quantum Mechanics

Introduction to Perturbation Theory in Quantum Mechanics

Arteca, G.A., Fernández, F.M., and Castro, E.A., Large Order Perturbation Theory and Summation Methods in Quantum Mechanics, in Lecture Notes in Chemistry, Vol. 53, SpringerVerlag, Berlin, 1990, chap. 9. Adams,B.G.,Algebraic Approach to ...

Author: Francisco M. Fernandez

Publisher: CRC Press

ISBN: 9781420039641

Category: Science

Page: 288

View: 873

Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation
Categories: Science

Algebraic Methods in Quantum Chemistry and Physics

Algebraic Methods in Quantum Chemistry and Physics

Kato, T, Perturbation Theory of Linear Operators, Springer-Verlag, Berlin, 1966. 39. Arteca, G. A., Fernández, F. M. and Castro, E. A., Large Order Perturbation Theory and Summation Methods in Quantum Mechanics, Lecture Notes in ...

Author: Francisco M. Fernandez

Publisher: CRC Press

ISBN: 9781000714845

Category: Mathematics

Page: 288

View: 162

Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.
Categories: Mathematics

Algebraic Approach to Simple Quantum Systems

Algebraic Approach to Simple Quantum Systems

With Applications to Perturbation Theory Barry G. Adams ... [AR90] Arteca, G.A., Fernández, F.M. and Castro, E.A. “Large Order Perturbation Theory and Summation Methods in Quantum Mechanics,” Lecture Notes in Chemistry, Vol.

Author: Barry G. Adams

Publisher: Springer Science & Business Media

ISBN: 9783642579332

Category: Science

Page: 451

View: 228

This book provides an introduction to the use of algebraic methods and sym bolic computation for simple quantum systems with applications to large order perturbation theory. It is the first book to integrate Lie algebras, algebraic perturbation theory and symbolic computation in a form suitable for students and researchers in theoretical and computational chemistry and is conveniently divided into two parts. The first part, Chapters 1 to 6, provides a pedagogical introduction to the important Lie algebras so(3), so(2,1), so(4) and so(4,2) needed for the study of simple quantum systems such as the D-dimensional hydrogen atom and harmonic oscillator. This material is suitable for advanced undergraduate and beginning graduate students. Of particular importance is the use of so(2,1) in Chapter 4 as a spectrum generating algebra for several important systems such as the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This approach provides an interesting and important alternative to the usual textbook approach using series solutions of differential equations.
Categories: Science

Weakly Nonlocal Solitary Waves and Beyond All Orders Asymptotics

Weakly Nonlocal Solitary Waves and Beyond All Orders Asymptotics

Generalized Solitons and Hyperasymptotic Perturbation Theory John P. Boyd. Arteca, G. A., Fernandez, F. M. and Castro, E. A.: 1990, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics, SpringerVerlag, New York.

Author: John P. Boyd

Publisher: Springer Science & Business Media

ISBN: 9781461558255

Category: Mathematics

Page: 596

View: 530

This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.
Categories: Mathematics

Mathematical Models and Methods for Ab Initio Quantum Chemistry

Mathematical Models and Methods for Ab Initio Quantum Chemistry

R. O. Ponec, Overlap Determinant Method in the Theory of Pericyclic Reactions. VIII, 126 pages. ... 53: G.A. Arteca, F.M. Fernández, E.A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics. XI, 644 pages.

Author: M. Defranceschi

Publisher: Springer Science & Business Media

ISBN: 9783642572371

Category: Science

Page: 244

View: 443

On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.
Categories: Science

Chemical Kinetics Beyond The Textbook

Chemical Kinetics  Beyond The Textbook

In addition to the problems described in Sections 3 and 4, we applied the method in investigating the ... G. A. Arteca, F. M. Fernández, and E. A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics.

Author: Lindenberg Katja

Publisher: World Scientific

ISBN: 9781786347022

Category: Science

Page: 620

View: 719

Processes involving randomly moving particles, which react either upon encounter or via distance-dependent reaction rates, are ubiquitous in nature. A few stray examples are recombination of ions or holes and electrons, excitation energy migration and quenching, trapping of particles by other species, coagulation, binding of ligands and proteins to specific sites, chemotaxis, catalytically-induced self-propulsion, polymerization, growth of dendrites or aggregates, or nuclei of a new phase.Several decades ago, it was recognized that the kinetic behavior in some systems with reactions and random transport is strongly affected by many factors, which were not taken into account in previous studies. These are, to name but a few, fluctuations in the spatial distributions of the reactants and fluctuations of the reactivity, some essentially many-particle phenomena, effects of anomalous diffusion, molecular crowding, as well as the internal geometry of the reaction bath. Within recent years, along with a growing interest in chemical processes ocurring in biological systems or cellular environments, numerous advances have been made and considerable knowledge has been acquired. These seminal contributions are, however, scattered among many journals and no attempt has been made so far to present a unified picture.This book presents a general overview of different contemporary facets of chemical kinetics in a variety of different environments. It includes 23 seminal works and reviews on different aspects of reaction processes in chemical, physical and biophysical systems, both theoretical and experimental.
Categories: Science

Methods in Reaction Dynamics

Methods in Reaction Dynamics

36: J. Ugi, J. Dugundji, R. Kopp and D. Marquarding, Perspectives in Theoretical Stereochemistry. ... 53: G.A. Arteca, F.M. Fernández, E.A. Castro, Large Order Perturbation Theory and Summation Methods in Quantum Mechanics.

Author: W. Jakubetz

Publisher: Springer Science & Business Media

ISBN: 9783642565113

Category: Science

Page: 195

View: 446

Methods in Reaction Dynamics is a collection of lectures given at the 1999 Mariapfarr Workshop in Theoretical Chemistry. Arranged as a series of detailed reviews, it provides an overview of quantum mechanical techniques used to describe and simulate the dynamics and kinetics of elementary chemical reactions. The volume provides in-depth discussions of selected topics in Theoretical Chemistry, such as quantum methods in theoretical and computational reaction dynamics and kinetics; time-dependent, time-independent and mixed quantum-classical techniques. Some of the topics have not been reviewed before in detail.
Categories: Science