› › Many Body Schrodinger Equation

Many-Body Schrödinger Equation

Author : Hiroshi Isozaki

Publisher : Springer Nature

Page : 411 pages

File Size : 34,11 MB

Release : 2023-08-28

Category : Science

ISBN : 9819937043

Get eBook

Book Description

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.



Many-Body Theory of Solids

Author : John C. Inkson

Publisher : Springer Science & Business Media

Page : 333 pages

File Size : 14,99 MB

Release : 2012-12-06

Category : Science

ISBN : 1475702264

Get eBook

Book Description

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.



Many-Body Quantum Theory in Condensed Matter Physics

Author : Henrik Bruus

Publisher : Oxford University Press

Page : 458 pages

File Size : 11,20 MB

Release : 2004-09-02

Category : Science

ISBN : 0198566336

Get eBook

Book Description

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.



Many-Body Schrödinger Dynamics of Bose-Einstein Condensates

Author : Kaspar Sakmann

Publisher : Springer Science & Business Media

Page : 135 pages

File Size : 23,16 MB

Release : 2011-08-31

Category : Science

ISBN : 3642228666

Get eBook

Book Description

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.



Many-body Theory Exposed! Propagator Description Of Quantum Mechanics In Many-body Systems (2nd Edition)

Author : Willem Hendrik Dickhoff

Publisher : World Scientific Publishing Company

Page : 851 pages

File Size : 17,43 MB

Release : 2008-05-02

Category : Science

ISBN : 9813101318

Get eBook

Book Description

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.



Elementary Methods of Molecular Quantum Mechanics

Author : Valerio Magnasco

Publisher : Elsevier

Page : 750 pages

File Size : 36,71 MB

Release : 2006-12-20

Category : Science

ISBN : 008046680X

Get eBook

Book Description

Elementary Methods of Molecular Quantum Mechanics shows the methods of molecular quantum mechanics for graduate University students of Chemistry and Physics. This readable book teaches in detail the mathematical methods needed to do working applications in molecular quantum mechanics, as a preliminary step before using commercial programmes doing quantum chemistry calculations.This book aims to bridge the gap between the classic Coulson's Valence, where application of wave mechanical principles to valence theory is presented in a fully non-mathematical way, and McWeeny's Methods of Molecular Quantum Mechanics, where recent advances in the application of quantum mechanical methods to molecular problems are presented at a research level in a full mathematical way. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each Chapter.* Uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics * Simplifies all mathematical formulae for the reader* Provides educational training in basic methodology



Ideas of Quantum Chemistry

Author : Lucjan Piela

Publisher : Elsevier

Page : 1122 pages

File Size : 43,53 MB

Release : 2006-11-28

Category : Science

ISBN : 0080466761

Get eBook

Book Description

Ideas of Quantum Chemistry shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field.Ideas of Quantum Chemistry has both textbook and reference work aspects. Like a textbook, the material is organized into digestable sections with each chapter following the same structure. It answers frequently asked questions and highlights the most important conclusions and the essential mathematical formulae in the text. In its reference aspects, it has a broader range than traditional quantum chemistry books and reviews virtually all of the pertinent literature. It is useful both for beginners as well as specialists in advanced topics of quantum chemistry. The book is supplemented by an appendix on the Internet.* Presents the widest range of quantum chemical problems covered in one book * Unique structure allows material to be tailored to the specific needs of the reader * Informal language facilitates the understanding of difficult topics



Optical Materials

Author : Joseph H. Simmons

Publisher : Academic Press

Page : 416 pages

File Size : 46,10 MB

Release : 2000

Category : Science

ISBN : 9780126441406

Get eBook

Book Description

Optical Materials presents, in a unified form, the underlying physical and structural processes that determine the optical behavior of materials. It does this by combining elements from physics, optics, and materials science in a seamless manner, and introducing quantum mechanics when needed. The book groups the characteristics of optical materials into classes with similar behavior. In treating each type of material, the text pays particular attention to atomic composition and chemical makeup, electronic states and band structure, and physical microstructure so that the reader will gain insight into the kinds of materials engineering and processing conditions that are required to produce a material exhibiting a desired optical property. The physical principles are presented on many levels, including a physical explanation, followed by formal mathematical support and examples and methods of measurement. The reader may overlook the equations with no loss of comprehension, or may use the text to find appropriate equations for calculations of optical properties. Presents the optical properties of metals, insulators, semiconductors, laser materials, and non-linear materials Physical processes are discussed and quantified using precise mathematical treatment, followed by examples and a discussion of measurement methods Authors combine many years of expertise in condensed matter physics, classical and quantum optics, and materials science The text is written on many levels and will benefit the novice as well as the expert Explains the concept of color in materials Explains the non-linear optical behavior of materials in a unified form Appendices present rigorous derivations



Solving the Schrodinger Equation

Author : Paul L. A. Popelier

Publisher : World Scientific

Page : 375 pages

File Size : 24,36 MB

Release : 2011

Category : Science

ISBN : 1848167253

Get eBook

Book Description

The Schrodinger equation is the master equation of quantum chemistry. The founders of quantum mechanics realised how this equation underpins essentially the whole of chemistry. However, they recognised that its exact application was much too complicated to be solvable at the time. More than two generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrodinger equation. Each method is based on a set of core ideas and this volume aims to explain these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method that combines the best of all worlds?



Density Functional Theory

Author : Reiner M. Dreizler

Publisher : Springer Science & Business Media

Page : 312 pages

File Size : 35,70 MB

Release : 2012-12-06

Category : Science

ISBN : 3642861059

Get eBook

Book Description

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.