Adiabatic Perturbation Theory In Quantum Dynamics

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Adiabatic Perturbation Theory In Quantum Dynamics

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Author : Stefan Teufel
language : en
Publisher: Springer
Release Date : 2003-12-09

Adiabatic Perturbation Theory In Quantum Dynamics written by Stefan Teufel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-09 with Science categories.

Focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit. A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.

Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics

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Author : Gianfausto Dell'Antonio
language : en
Publisher: Springer
Release Date : 2016-05-24

Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics written by Gianfausto Dell'Antonio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Science categories.

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Multiscale Methods In Quantum Mechanics

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Author : Philippe Blanchard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Multiscale Methods In Quantum Mechanics written by Philippe Blanchard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.

Lectures On The Mathematics Of Quantum Mechanics I

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Author : Gianfausto Dell'Antonio
language : en
Publisher: Springer
Release Date : 2015-05-25

Lectures On The Mathematics Of Quantum Mechanics I written by Gianfausto Dell'Antonio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-25 with Science categories.

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Quantum Chemistry And Dynamics Of Excited States

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Author : Leticia González
language : en
Publisher: John Wiley & Sons
Release Date : 2021-02-01

Quantum Chemistry And Dynamics Of Excited States written by Leticia González and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-01 with Science categories.

An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

Mathematical Physics Of Quantum Mechanics

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Author : Joachim Asch
language : en
Publisher: Springer
Release Date : 2006-09-09

Mathematical Physics Of Quantum Mechanics written by Joachim Asch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-09 with Science categories.

At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.

Applied Quantum Mechanics

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Author : Walter A Harrison
language : en
Publisher: World Scientific Publishing Company
Release Date : 2000-07-24

Applied Quantum Mechanics written by Walter A Harrison and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-24 with Science categories.

Quantum mechanics is widely recognized as the basic law which governs all of nature, including all materials and devices. It has always been essential to the understanding of material properties, and as devices become smaller it is also essential for studying their behavior. Nevertheless, only a small fraction of graduate engineers and materials scientists take a course giving a systematic presentation of the subject. The courses for physics students tend to focus on the fundamentals and formal background, rather than on application, and do not fill the need. This invaluable text has been designed to fill the very apparent gap.The book covers those parts of quantum theory which may be necessary for a modern engineer. It focuses on the approximations and concepts which allow estimates of the entire range of properties of nuclei, atoms, molecules, and solids, as well as the behavior of lasers and other quantum-optic devices. It may well prove useful also to graduate students in physics, whose courses on quantum theory tend not to include any of these applications. The material has been the basis of a course taught to graduate engineering students for the past four years at Stanford University.Topics Discussed: Foundations; Simple Systems; Hamiltonian Mechanics; Atoms and Nuclei; Molecules; Crystals; Transitions; Tunneling; Transition Rates; Statistical Mechanics; Transport; Noise; Energy Bands; Electron Dynamics in Solids; Vibrations in Solids; Creation and Annihilation Operators; Phonons; Photons and Lasers; Coherent States; Coulomb Effects; Cooperative Phenomena; Magnetism; Shake-off Excitations; Exercise Problems.A supplementary Instructor's Solutions Manual is available for this book.

Introduction To Perturbation Theory In Quantum Mechanics

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Author : Francisco M. Fernandez
language : en
Publisher: CRC Press
Release Date : 2000-09-19

Introduction To Perturbation Theory In Quantum Mechanics written by Francisco M. Fernandez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-19 with Science categories.

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 “/p>

Perturbation Theory

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Author : Giuseppe Gaeta
language : en
Publisher: Springer Nature
Release Date : 2022-12-16

Perturbation Theory written by Giuseppe Gaeta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Mathematical Concepts Of Quantum Mechanics

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Author : Stephen J. Gustafson
language : en
Publisher: Springer Nature
Release Date : 2020-10-21

Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-21 with Mathematics categories.

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.