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Author : Peter R. Surjan
ISBN : 9783642747557
Genre : Science
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The aim of this book is to give a simple, short, and elementary introduction to the second quantized formalism as applied to a many-electron system. It is intended for those, mainly chemists, who are familiar with traditional quantum chemistry but have not yet become acquainted with second quantization. The treatment is, in part, based on a series of seminars held by the author on the subject. It has been realized that many quantum chemists either interested in theory or in applications, being educated as chemi~ts and not as physicists, have never devoted themselves to taking a course on the second quantized approach. Most available textbooks on this topic are not very easy to follow for those who are not trained in theory, or they are not detailed enough to offer a comprehensive treatment. At the same time there are several papers in quantum chemical literature which take advantage of using second quantization, and it would be worthwhile if those papers were accessible for a wider reading public. For this reason, it is intended in this survey to review the basic formalism of second quantization, and to treat some selected chapters of quantum chemistry in this language. Most derivations will be carried out in a detailed manner, so the reader need not accept gaps to understand the result.

Second Quantization-Based Methods in Quantum Chemistry presents several modern quantum chemical tools that are being applied to electronic states of atoms and molecules. Organized into six chapters, the book emphasizes the quantum chemical methods whose developments and implementations have been presented in the language of second quantization. The opening chapter of the book examines the representation of the electronic Hamiltonian, other quantum-mechanical operators, and state vectors in the second-quantization language. This chapter also describes the unitary transformations among orthonormal orbitals in an especially convenient manner. In subsequent chapters, various tools of second quantization are used to describe many approximation techniques, such as Hartree-Fock, perturbation theory, configuration interaction, multiconfigurational Hartree-Fock, cluster methods, and Green’s function. This book is an invaluable source for researchers in quantum chemistry and for graduate-level students who have already taken introductory courses that cover the fundamentals of quantum mechanics through the Hartree-Fock method as applied to atoms and molecules.

Author : K. P. Lawley
ISBN : 9780470143384
Genre : Science
File Size : 72.9 MB
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The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman -- Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbationexpansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chem-Simons theory of particles with fractional statistics (anyohs) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous Black -- Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.

Author : Björn O. Roos
ISBN : 9783642581502
Genre : Science
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"Quantum Chemistry" is the course material of a European Summer School in Quantum Chemistry, organized by Bj|rn O. Roos. It consists of lectures by outstanding scientists who participate in the education of students and young scientists. The book has a wider appeal as additional reading for University courses. Contents: P.-A. Malmquist: Mathematical Tools in Quantum Chemistry J. Olsen: The Method of Second Quantization P.R. Taylor: Molecular Symmetry and Quantum Chemistry B.O. Roos: The Multiconfigurational (MC) Self-Consistent Field (SCF) Theory P.E.M. Siegbahn: The Configuration Interaction Method T. Helgaker: Optimization of Minima and Saddle Points P.R. Taylor: Accurate Calculations and Calibration U. Wahlgren: Effective Core Potential Method

Author : J. J. Sakurai
ISBN : 9781108527422
Genre : Science
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Modern Quantum Mechanics is a classic graduate level textbook, covering the main quantum mechanics concepts in a clear, organized and engaging manner. The author, Jun John Sakurai, was a renowned theorist in particle theory. The second edition, revised by Jim Napolitano, introduces topics that extend the text's usefulness into the twenty-first century, such as advanced mathematical techniques associated with quantum mechanical calculations, while at the same time retaining classic developments such as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequality. A solution manual for instructors using this textbook can be downloaded from www.cambridge.org/9781108422413.

Author : George G. Hall
ISBN : 3540537929
Genre : Science
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This book originated from a course which I developed for the Master's degree course in Molecular Engineering in Kyoto University. Most of the students had degrees in Chemistry and a limited experience of Physics and Mathematics. Since research in Molecular Engineering requires knowledge of some applications of solid state physics which are not treated in conventional physics texts it was necessary to devise a course which would build on their chemical background and enable them to read the contemporary literature of relevance to their research. I hope that this book will be found useful as a text for other advanced courses on material science for chemists. Molecular Engineering is concerned with the design and construction, at the molecular level, of materials which can fulfil specific functions. Thus the study of the forces between molecules and the influence of molecular shapes and electrostatic features on molecular properties are important. The mechanisms whereby, in the solid state, these produce cooperative effects, catalytic effects and abnormal electrical effects must be understood, at least qualitatively. The aim of this book has been to give insight into the mechanisms whereby molecules influence one another when they are close together.

Author : Edward G Harris
ISBN : 9780486793290
Genre : Science
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Introductory text for graduate students in physics taking a year-long course in quantum mechanics in which the third quarter is devoted to relativistic wave equations and field theory. Answers to selected problems. 1972 edition.

Examines the intersection of quantum information and chemical physics The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics. This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science community. It examines topics in quantum computation and quantum information that are related to or intersect with key topics in chemical physics. The reviews address both what chemistry can contribute to quantum information and what quantum information can contribute to the study of chemical systems, surveying both theoretical and experimental quantum information research within the field of chemical physics. With contributions from an international team of leading experts, Volume 154 offers seventeen detailed reviews, including: Introduction to quantum information and computation for chemistry Quantum computing approach to non-relativistic and relativistic molecular energy calculations Quantum algorithms for continuous problems and their applications Photonic toolbox for quantum simulation Vibrational energy and information transfer through molecular chains Tensor networks for entanglement evolution Reviews published in Advances in Chemical Physics are typically longer than those published in journals, providing the space needed for readers to fully grasp the topic: the fundamentals as well as the latest discoveries, applications, and emerging avenues of research. Extensive cross-referencing enables readers to explore the primary research studies underlying each topic.

Author : Michael Bitbol
ISBN : 9789400917729
Genre : History
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This book is the final outcome of two projects. My first project was to publish a set of texts written by Schrodinger at the beginning of the 1950's for his seminars and lectures at the Dublin Institute for Advanced Studies. These almost completely forgotten texts contained important insights into the interpretation of quantum mechanics, and they provided several ideas which were missing or elusively expressed in SchrOdinger's published papers and books of the same period. However, they were likely to be misinterpreted out of their context. The problem was that current scholarship could not help very much the reader of these writings to figure out their significance. The few available studies about SchrOdinger's interpretation of quantum mechanics are generally excellent, but almost entirely restricted to the initial period 1925-1927. Very little work has been done on Schrodinger's late views on the theory he contributed to create and develop. The generally accepted view is that he never really recovered from his interpretative failure of 1926-1927, and that his late reflections (during the 1950's) are little more than an expression of his rising nostalgia for the lost ideal of picturing the world, not to say for some favourite traditional picture. But the content and style of Schrodinger's texts of the 1950's do not agree at all with this melancholic appraisal; they rather set the stage for a thorough renewal of accepted representations. In order to elucidate this paradox, I adopted several strategies.

Author : Vishnu S. Mathur
ISBN : 1420078739
Genre : Science
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Taking a conceptual approach to the subject, Concepts in Quantum Mechanics provides complete coverage of both basic and advanced topics. Following in the footsteps of Dirac’s classic work Principles of Quantum Mechanics, it explains all themes from first principles. The authors present alternative ways of representing the state of a physical system, outline the mathematical connection between the representatives of the same state in different representations, and highlight the connection between Dirac brackets and their integral forms in the coordinate and momentum representations. They also logically develop the equations of motion in Schrödinger and Heisenberg pictures. In addition, the book covers motion in the presence of potential steps and wells, bound state problems, symmetries and their consequences, the role of angular momentum in quantum mechanics, approximation methods, time-dependent perturbation methods, and second quantization. Written by authoritative professors who have taught quantum mechanics at the graduate level for a combined forty years, this textbook provides students with a strong foundation in quantum mechanics. After reading the book, students will be ready to take on quantum field theory.

This work presents a comprehensive overview of the present state of research in computational chemistry. Comprising 52 chapters, it includes the development of new formalisms, numerical calculations, analysis of results and interpretation of physical/chemical phenomena, all of which reflects the work being carried out at laboratories throughout the world. Computational Chemistry may be used as a textbook in graduate courses, e.g. on solids, where the course material can be complemented by the chapters on superconductors, metals ionic solids, imperfect crystals, insulators and polymers. As a reference work, a specific chapter will acquaint the reader with the goals of research in a particular field, the formulation best adapted (at present) for that task, and the quality of the results which may be obtained. Further reading of the selected references given in the chapter will lead to a detailed knowledge of the field. The complementary character of the chapters is best exemplified by the mention of subjects such as configuration interaction treatments (in general for atoms, for simple molecules), biological receptors and drug design (intermolecular potentials, quantum similarity, shape analysis solvent effects, modelling), spectroscopy (Raman and infrared, NMR, photoelectron), chemical reactions (classical trajectories, reactivity, heterogeneous catalysis), etc.

Author : Willem Hendrik Dickhoff
ISBN : 9789812813794
Genre : Science
File Size : 43.85 MB
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This comprehensive textbook on the quantum mechanics of identical particles includes a wealth of valuable experimental data, in particular recent results from direct knockout reactions directly related to the single-particle propagator in many-body theory. The comparison with data is incorporated from the start, making the abstract concept of propagators vivid and accessible. Results of numerical calculations using propagators or Green's functions are also presented. The material has been thoroughly tested in the classroom and the introductory chapters provide a seamless connection with a one-year graduate course in quantum mechanics. While the majority of books on many-body theory deal with the subject from the viewpoint of condensed matter physics, this book emphasizes finite systems as well and should be of considerable interest to researchers in nuclear, atomic, and molecular physics. A unified treatment of many different many-body systems is presented using the approach of self-consistent Green's functions. The second edition contains an extensive presentation of finite temperature propagators and covers the technique to extract the self-energy from experimental data as developed in the dispersive optical model.The coverage proceeds systematically from elementary concepts, such as second quantization and mean-field properties, to a more advanced but self-contained presentation of the physics of atoms, molecules, nuclei, nuclear and neutron matter, electron gas, quantum liquids, atomic Bose-Einstein and fermion condensates, and pairing correlations in finite and infinite systems, including finite temperature.

Author : Alexander Altland
ISBN : 9780521769754
Genre : Science
File Size : 84.96 MB
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This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Author : Daniel Greenberger
ISBN : 3540706267
Genre : Science
File Size : 40.92 MB
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With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.

Author : Willem H Dickhoff
ISBN : 9789813106499
Genre : Science
File Size : 55.81 MB
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Standard textbooks on the many-body problem do not include a wealth of valuable experimental data, in particular recent results from direct knockout reactions, which are directly related to the single-particle propagator in many-body theory. In this indispensable book, the comparison with experimental data is incorporated from the start, making the abstract concept of propagators vivid and comprehensible. The discussion of numerical calculations using propagators or Green's functions, also absent from current textbooks, is presented in this book. Much of the material has been tested in the classroom and the introductory chapters allow a seamless connection with a one-year graduate course in quantum mechanics. While the majority of books on many-body theory deal with the subject from the viewpoint of condensed matter physics, this book also emphasizes finite systems and should be of considerable interest to researchers in nuclear, atomic, and molecular physics. A unified treatment of many different many-body systems is presented using the approach of self-consistent Green's functions. Several topics, not available in other books, in particular the description of atomic Bose–Einstein condensates, have been included. The coverage proceeds in a systematic way from elementary concepts, such as second quantization and mean-field properties, to a more advanced but self-contained presentation of the physics of atoms, molecules, nuclei, nuclear and neutron matter, electron gas, quantum liquids, atomic Bose–Einstein and fermion condensates, and pairing correlations in finite and infinite systems.