Download or read book Variational Principles and Methods in Theoretical Physics and Chemistry written by Robert K. Nesbet and published by Cambridge University Press. This book was released on 2002-11-14 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly suitable as a backup reference for lecture courses in mathematical methods in physics and theoretical chemistry.

Download or read book Variational Principles in Dynamics and Quantum Theory written by Wolfgang Yourgrau and published by Courier Corporation. This book was released on 2012-04-26 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div

Download or read book Variational Methods in Mathematical Physics written by Philippe Blanchard and published by Springer Verlag. This book was released on 1992 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Variational Methods in Molecular Modeling written by Jianzhong Wu and published by Springer. This book was released on 2016-12-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical understanding rather than on rigorous mathematical derivations, the content is accessible to graduate students and researchers in the broad areas of materials science and engineering, chemistry, chemical and biomolecular engineering, applied mathematics, condensed-matter physics, without specific training in theoretical physics or calculus of variations.

Download or read book Statistical Mechanics And The Physics Of Many particle Model Systems written by Kuzemsky Alexander Leonidovich and published by World Scientific. This book was released on 2017-02-24 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.

Download or read book Variational Principles in Physics written by Tamás Sándor Biró and published by Springer Nature. This book was released on 2023-03-22 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an English translation from a Hungarian book designed for graduate and postgraduate students about the use of variational principles in theoretical physics. Unlike many academic textbooks, it dashes across several lecture disciplines taught in physics courses. It emphasizes and demonstrates the use of the variational technique and philosophy behind the basic laws in mechanics, relativity theory, electromagnetism, and quantum mechanics. The book is meant for advanced students and young researchers in theoretical physics but, also, more experienced researchers can benefit from its reading.

Download or read book Variational Methods with Applications in Science and Engineering written by Kevin W. Cassel and published by Cambridge University Press. This book was released on 2013-07-22 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Download or read book The Nature of Motive Force written by Achintya Kumar Pramanick and published by Springer. This book was released on 2014-08-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph Prof. Pramanick explicates the law of motive force, a fundamental law of nature that can be observed and appreciated as an addition to the existing laws of thermodynamics. This unmistakable and remarkable tendency of nature is equally applicable to all other branches of studies. He first conceptualized the law of motive force in 1989, when he was an undergraduate student. Here he reports various applications of the law in the area of thermodynamics, heat transfer, fluid mechanics and solid mechanics, and shows how it is possible to solve analytically century-old unsolved problems through its application. This book offers a comprehensive account of the law and its relation to other laws and principles, such as the generalized conservation principle, variational formulation, Fermat’s principle, Bejan’s constructal law, entropy generation minimization, Bejan’s method of intersecting asymptotes and equipartition principle. Furthermore, the author addresses some interrelated fundamental problems of contemporary interest, especially to thermodynamicists, by combining analytical methods, physical reasoning and the proposed law of motive force. This foundational work is a valuable reading for both students and researchers in exact as well as non-exact sciences and, at the same time, a pleasant learning experience for the novice.

Download or read book The Variational Principles of Mechanics written by Lánczos Kornél and published by . This book was released on 1952 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Variational Principles in Physics written by Jean-Louis Basdevant and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and enhanced new edition of a well-established textbook provides a balanced overview of various areas of theoretical physics based on the use of variational principles. As well as field theory, the book deals with motion in curved spaces, the cradle of general relativity, and gravitational optics. New chapters on the relation of classical mechanics and geometrical optics as well as gravitational waves, which are considered as a true confirmation of general relativity, have been included. Each chapter has been carefully revised and enlarged. Finally, the text describes Feynman's formulation of quantum mechanics by path integrals, which gives the link between quantum and classical mechanics. The book provides a set of exercises, problems, and solutions.

Download or read book Theoretical Analyses Computations and Experiments of Multiscale Materials written by Ivan Giorgio and published by Springer Nature. This book was released on 2022-05-03 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the 60th birthday of the Prof. Francesco dell’Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.

Download or read book An Introduction to Lagrangian Mechanics written by Alain Jean Brizard and published by World Scientific. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler?Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.This textbook is suitable for undergraduate students who have acquired the mathematical skills needed to complete a course in Modern Physics.

Download or read book An Introduction to Lagrangian Mechanics written by Alain J Brizard and published by World Scientific Publishing Company. This book was released on 2014-11-28 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler–Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory. The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics. New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

Download or read book Variational Methods in Electron Atom Scattering Theory written by Robert K. Nesbet and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena.

Download or read book Quantum Nanochemistry Volume One written by Mihai V. Putz and published by CRC Press. This book was released on 2016-03-30 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 of the 5-volume Quantum Nanochemistry set presents an overall perspective of nuclear, atomic, molecular, and solids structures, and the observability and quantum properties as based on the quantum principles in their various levels of applications, from Planck, Bohr, Einstein, Schrödinger, Hartree-Fock, up to Feynman Path Integral approaches. The volume presents in a balanced manner the fundamental and advanced concepts, principles, and models as well as their first and novel combinations and applications in modeling complex natural or designed phenomena.

Download or read book Perspectives on Structure and Mechanism in Organic Chemistry written by Felix A. Carroll and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helps to develop new perspectives and a deeper understanding oforganic chemistry Instructors and students alike have praised Perspectives onStructure and Mechanism in Organic Chemistry because itmotivates readers to think about organic chemistry in new andexciting ways. Based on the author's first hand classroomexperience, the text uses complementary conceptual models to givenew perspectives on the structures and reactions of organiccompounds. The first five chapters of the text discuss the structure andbonding of stable molecules and reactive intermediates. These arefollowed by a chapter exploring the methods that organic chemistsuse to study reaction mechanisms. The remaining chapters examinedifferent types of acid-base, substitution, addition, elimination,pericyclic, and photochemical reactions. This Second Edition has been thoroughly updated andrevised to reflect the latest findings in physical organicchemistry. Moreover, this edition features: New references to the latest primary and review literature More study questions to help readers better understand andapply new concepts in organic chemistry Coverage of new topics, including density functional theory,quantum theory of atoms in molecules, Marcus theory, molecularsimulations, effect of solvent on organic reactions, asymmetricinduction in nucleophilic additions to carbonyl compounds, anddynamic effects on reaction pathways The nearly 400 problems in the text do more than allow studentsto test their understanding of the concepts presented in eachchapter. They also encourage readers to actively review andevaluate the chemical literature and to develop and defend theirown ideas. With its emphasis on complementary models and independentproblem-solving, this text is ideal for upper-level undergraduateand graduate courses in organic chemistry.

Download or read book Electron Dynamics in Molecular Interactions written by Frank Hagelberg and published by World Scientific. This book was released on 2013-12-23 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to the theory of electronic motion in molecular processes — an increasingly relevant and rapidly expanding segment of molecular quantum dynamics. Emphasis is placed on describing and interpreting transitions between electronic states in molecules as they occur typically in cases of reactive scattering between molecules, photoexcitation or nonadiabatic coupling between electronic and nuclear degrees of freedom. Electron Dynamics in Molecular Interactions aims at a synoptic presentation of some very recent theoretical efforts to solve the electronic problem in quantum molecular dynamics, contrasting them with more traditional schemes. The presented models are derived from their roots in basic quantum theory, their interrelations are discussed, and their characteristic applications to concrete chemical systems are outlined. This volume also includes an assessment of the present status of electron dynamics and a report on novel developments to meet the current challenges in the field. Further, this monograph responds to a need for a systematic comparative treatise on nonadiabatic theories of quantum molecular dynamics, which are of considerably higher complexity than the more traditional adiabatic approaches and are steadily gaining in importance. This volume addresses a broad readership ranging from physics or chemistry graduate students to specialists in the field of theoretical quantum dynamics. Contents:Preparations:Ab Initio Theory of Electronic StructureThe Adiabatic and the Diabatic RepresentationBasic Concepts of Scattering TheorySemiclassical NotionsOpen Systems: Elements of Rate TheoryMethods:Time-Independent Theory of Molecular Collisions I: Multichannel ScatteringTime-Independent Theory of Molecular Collisions II: The Electronic ProblemThe Time-Dependent Self-consistent Field TheoryEvolution of Coherent Molecular States: Electron Nuclear Dynamics TheoryThe Classical Electron AnalogHopping and SpawningSemiclassical Propagator TechniquesQuantum Hydrodynamics I: Coupled Trajectories in Bohmian MechanicsQuantum Hydrodynamics II: The Semiclassical Liouville-Von Neumann EquationWavepacket Propagation MethodsDensity Functional DynamicsDecoherenceSpecial Topics:Ultrafast Optical SpectroscopyOptical Control of Electron Multistate Molecular DynamicsElectron Transfer in Condensed MediaElectronic Friction in Molecule-Surface Interactions Readership: Graduate students and researchers in physical chemistry and computational physics; industrial chemists and physicists interested in the field. Key Features:This book provides an overview of the recent nonadiabatic theories of quantum molecular dynamics that are widely used and highly acknowledged in the community of physical chemistsThere is currently no other book available in the market that shares the publication scope of this bookIt can be used as a supplementary textbook to graduate level course in quantum chemistry or chemical dynamicsKeywords:Nonadiabatic Processes;Electronic Transitions;Molecular Dynamics;Quantum Trajectories;Wavepacket Propagation