Download or read book Many Body Schr dinger Equation written by Hiroshi Isozaki and published by Springer Nature. This book was released on 2023-08-28 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral properties for Schrödinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the few-particle systems, we now have sufficient knowledge for two-body systems, although much less is known about N-body systems. The asymptotic completeness of time-dependent wave operators was proved in the 1980s and was a landmark in the study of the N-body problem. However, many problems are left open for the stationary N-particle equation. Due to the recent rapid development of computer power, it is now possible to compute the three-body scattering problem numerically, in which the stationary formulation of scattering is used. This means that the stationary theory for N-body Schrödinger operators remains an important problem of quantum mechanics. It is stressed here that for the three-body problem, we have a satisfactory stationary theory. This book is devoted to the mathematical aspects of the N-body problem from both the time-dependent and stationary viewpoints. The main themes are:(1) The Mourre theory for the resolvent of self-adjoint operators(2) Two-body Schrödinger operators—Time-dependent approach and stationary approach(3) Time-dependent approach to N-body Schrödinger operators(4) Eigenfunction expansion theory for three-body Schrödinger operatorsCompared with existing books for the many-body problem, the salient feature of this book consists in the stationary scattering theory (4). The eigenfunction expansion theorem is the physical basis of Schrödinger operators. Recently, it proved to be the basis of inverse problems of quantum scattering. This book provides necessary background information to understand the physical and mathematical basis of Schrödinger operators and standard knowledge for future development.
Download or read book Many Body Theory of Solids written by John C. Inkson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: here exists a gap in the present literature on quantum mechanics T and its application to solids. It has been difficult to find an intro ductory textbook which could take a student from the elementary quan tum mechanical ideas of the single-particle Schrodinger equations, through the formalism and new physical concepts of many-body theory, to the level where the student would be equipped to read the scientific literature and specialized books on specific topics. The present book, which I believe fills this gap, grew out of two courses which I have given for a number of years at the University of Cambridge: "Advanced Quan tum Mechanics," covering the quantization of fields, representations, and creation and annihilation operators, and "Many Body Theory," on the application of quantum field theory to solids. The first course is a final-year undergraduate physics course while the second is a joint first and fourth-year undergraduate math year postgraduate physics course ematics course. In an American context this would closely correspond to a graduate course at the masters level. In writing this book I have tried to stress the physical aspects of the mathematics preferring where possible to introduce a technique by using a simple illustrative example rather than develop a purely formal treat ment. In order to do this I have assumed a certain familiarity with solid state physics on the level of a normal undergraduate course, but the book should also be useful to those without such a background.
Download or read book Exactly Solvable Models In Many body Theory written by Norman H March and published by World Scientific. This book was released on 2016-05-27 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Download or read book Many Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
Download or read book The Many body Problem written by Daniel Charles Mattis and published by World Scientific. This book was released on 1993 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space ? such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz ? can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
Download or read book Many Body Schr dinger Dynamics of Bose Einstein Condensates written by Kaspar Sakmann and published by Springer Science & Business Media. This book was released on 2011-08-31 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: At extremely low temperatures, clouds of bosonic atoms form what is known as a Bose-Einstein condensate. Recently, it has become clear that many different types of condensates -- so called fragmented condensates -- exist. In order to tell whether fragmentation occurs or not, it is necessary to solve the full many-body Schrödinger equation, a task that remained elusive for experimentally relevant conditions for many years. In this thesis the first numerically exact solutions of the time-dependent many-body Schrödinger equation for a bosonic Josephson junction are provided and compared to the approximate Gross-Pitaevskii and Bose-Hubbard theories. It is thereby shown that the dynamics of Bose-Einstein condensates is far more intricate than one would anticipate based on these approximations. A special conceptual innovation in this thesis are optimal lattice models. It is shown how all quantum lattice models of condensed matter physics that are based on Wannier functions, e.g. the Bose/Fermi Hubbard model, can be optimized variationally. This leads to exciting new physics.
Download or read book Many Body Methods in Quantum Chemistry written by Uzi Kaldor and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the text of the invited lectures presented at the Symposium on Many Body Methods in Quantum Chemistry, held on the campus of Tel Aviv University in August 1988. The Symposium was a satellite meeting of the Sixth International Congress on Quantum Chemistry held in Jerusalem. The development and application of many-body methods in Quantum chemistry have been on the rise for a number of years. This is therefore a good time for an interim report on the state of the field. It is hoped that such a report is hereby provided, though it may not be complete. The Symposium was held under the auspices of Tel Aviv University, Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry. Other sponsors were the Israeli Academy of Sciences and Humanities, and the Israeli Ministry of Science and Development. Many thanks go to all of them. Finally, I would like to thank all the speakers and participants for making the meeting the enjoyable and (I hope) profitable experience it was. Tel Aviv, Israel Uzi Kaldor TESTS AND APPLICATIONS OF COMPLETE MODEL SPACE QUASIDEGENERATE MANY-BODY PERTURBATION THEORY FOR MOLECULES Karl F. Freed The James Franck Institute and Department of Chemistry The University of Chicago, Chicago, DUnois 60637 U.S.A.
Download or read book Introduction to Modern Methods of Quantum Many body Theory and Their Applications written by A. Fabrocini and published by World Scientific. This book was released on 2002 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains pedagogical articles on the dominant non-stochastic methods of microscopic many-body theories: Density functional theory, coupled cluster theory, and correlated basis functions methods in their widest sense. Further articles introduce students to applications of these methods in front -- line research such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics of current relevance. The book addresses the striking lack of pedagogical reference literature in the field that allows researchers to acquire the requisite physical insight and technical skills. The volume should, therefore, not only researchers to acquire the requisite physical insight and technical skills. The volume should, therefore, not only serve as a collection of information relevant to those who attended the school, but it provides be useful reference material to a broad range of theoretical physicists in condensed matter and nuclear theory.
Download or read book The Quantum Mechanics of Many Body Systems written by D.J. Thouless and published by Courier Corporation. This book was released on 2014-01-15 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Unabridged republication of the second edition of the work, originally published in the Pure and applied physics series by Academic Press, Inc., New York, in 1972"--Title page verso.
Download or read book Quantum Theory of Many Body Systems written by Alexandre Zagoskin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for graduates in physics and related fields, this is a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory, and the Matsubara, Keldysh, and Nambu-Gorov formalisms. The aim is not to be exhaustive, but to present just enough detail to enable students to follow the current research literature or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout the volume, and which therefore provides an ideal testing ground for many-body theories. '
Download or read book Many body Theory Exposed Propagator Description Of Quantum Mechanics In Many body Systems 2nd Edition written by Willem Hendrik Dickhoff and published by World Scientific Publishing Company. This book was released on 2008-05-02 with total page 851 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Density Functional Theory written by Reiner M. Dreizler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density Functional Theory is a rapidly developing branch of many-particle physics that has found applications in atomic, molecular, solid-state and nuclear physics. This book describes the conceptual framework of density functional theory and discusses in detail the derivation of explicit functionals from first principles as well as their application to Coulomb systems. Both non-relativistic and relativistic systems are treated. The connection of density functional theory with other many-body methods is highlighted. The presentation is self-contained; the book is, thus, well suited for a graduate course on density functional theory.
Download or read book Fundamentals of Many body Physics written by Wolfgang Nolting and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the present course on “Fundamentals of Theoretical Physics” is to be a direct accompaniment to the lower-division study of physics, and it aims at providing the ph- ical tools in the most straightforward and compact form as needed by the students in order to master theoretically more complex topics and problems in advanced studies and in research. The presentation is thus intentionally designed to be suf?ciently detailed and self-contained – sometimes, admittedly, at the cost of a certain elegance – to permit in- vidual study without reference to the secondary literature. This volume deals with the quantum theory of many-body systems. Building upon a basic knowledge of quantum mechanics and of statistical physics, modern techniques for the description of interacting many-particle systems are developed and applied to various real problems, mainly from the area of solid-state physics. A thorough revision should guarantee that the reader can access the relevant research literature without experiencing major problems in terms of the concepts and vocabulary, techniques and deductive methods found there. The world which surrounds us consists of very many particles interacting with one another, and their description requires in principle the solution of a corresponding number ofcoupledquantum-mechanicalequationsofmotion(Schrodinger ̈ equations),which,h- ever, is possible only in exceptional cases in a mathematically strict sense. The concepts of elementary quantum mechanics and quantum statistics are therefore not directly applicable in the form in which we have thus far encountered them. They require an extension and restructuring, which is termed “many-body theory”.
Download or read book Schr dinger Operators written by Erik Balslev and published by Springer. This book was released on 1992 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Back of the envelope Quantum Mechanics With Extensions To Many body Systems Integrable Pdes And Rare And Exotic Methods Second Edition written by Maxim Olchanyi (Olshanii) and published by World Scientific. This book was released on 2024-01-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that 'something else' is needed to quickly gain insight into the system they are going to study. Qualitative methods are this 'something else', but typically, students have never heard of them before.The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pièce de résistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear Schrödinger breather as a function of its width.A new theme that appears in the second edition are the rare and exotic methods in elementary quantum mechanics. The new chapter covers quantum-mechanical supersymmetry, power index method, scale invariance, self-similarity, and circle inversion.
Download or read book A Pedestrian Approach to Quantum Field Theory written by Edward G Harris and published by Courier Corporation. This book was released on 2014-03-05 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Time Dependent Density Functional Theory written by Carsten Ullrich and published by Oxford University Press. This book was released on 2012 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-dependent density-functional theory (TDDFT) is a quantum mechanical approach for the dynamical properties of electrons in matter. It's widely used in (bio)chemistry and physics to calculate molecular excitation energies and optical properties of materials. This is the first graduate-level text on the formal framework and applications of TDDFT.
