Density Matrix Theory And Applications

Author : Karl Blum
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 48,5 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781475749311

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Density Matrix Theory and Applications by Karl Blum Pdf

Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary variables. The use of density matrix methods also has the advan tage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incompletely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Author : Anonim
Publisher : Unknown
Page : 364 pages
File Size : 46,8 Mb
Release : 2012-01-21
Category : Electronic
ISBN : 3642205623

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Density Matrix Theory and Applications by Anonim Pdf

Author : Karl Blum
Publisher : Unknown
Page : 232 pages
File Size : 40,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1461568099

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Density Matrix Theory and Applications by Karl Blum Pdf

Author : Karl Blum
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 42,9 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781461568087

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Density Matrix Theory and Applications by Karl Blum Pdf

Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Author : Thomas Clark Farrar,John E. Harriman
Publisher : Unknown
Page : 191 pages
File Size : 40,9 Mb
Release : 1991
Category : Density matrices
ISBN : 091790303X

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Density Matrix Theory and Its Applications in NMR Spectroscopy by Thomas Clark Farrar,John E. Harriman Pdf

Author : Thomas C. Farrar,John E. Harriman
Publisher : Unknown
Page : 128 pages
File Size : 46,9 Mb
Release : 1992
Category : Electronic
ISBN : OCLC:637196582

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Density Matrix Theory and Its Applications in NMR Spectroscopy by Thomas C. Farrar,John E. Harriman Pdf

Author : David A. Mazziotti
Publisher : John Wiley & Sons
Page : 300 pages
File Size : 53,6 Mb
Release : 2007-04-06
Category : Science
ISBN : 9780470106594

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Reduced-Density-Matrix Mechanics by David A. Mazziotti Pdf

An up-to-date account of this cutting-edge research in a consistent and understandable framework, of special interest to experts in other areas of electronic structure and/or quantum many-body theory. It will serve equally well as a self-contained guide to learning about reduced density matrices either through self-study or in a classroom as well as an invaluable resource for understanding the critical advancements in the field.

Author : Nazmul Islam,Savas Kaya
Publisher : CRC Press
Page : 371 pages
File Size : 55,5 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9781351360234

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Conceptual Density Functional Theory and Its Application in the Chemical Domain by Nazmul Islam,Savas Kaya Pdf

In this book, new developments based on conceptual density functional theory (CDFT) and its applications in chemistry are discussed. It also includes discussion of some applications in corrosion and conductivity and synthesis studies based on CDFT. The electronic structure principles—such as the electronegativity equalization principle, the hardness equalization principle, the electrophilicity equalization principle, and the nucleophilicity equalization principle, along studies based on these electronic structure principles—are broadly explained. In recent years some novel methodologies have been developed in the field of CDFT. These methodologies have been used to explore mutual relationships between the descriptors of CDFT, namely electronegativity, hardness, etc. The mutual relationship between the electronegativity and the hardness depend on the electronic configuration of the neutral atomic species. The volume attempts to cover almost all such methodology. Conceptual Density Function Theory and Its Application in the Chemical Domain will be an appropriate guide for research students as well as the supervisors in PhD programs. It will also be valuable resource for inorganic chemists, physical chemists, and quantum chemists. The reviews, research articles, short communications, etc., covered by this book will be appreciated by theoreticians as well as experimentalists.

Author : Fumio Hiai,Dénes Petz
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 53,9 Mb
Release : 2014-02-06
Category : Mathematics
ISBN : 9783319041506

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Introduction to Matrix Analysis and Applications by Fumio Hiai,Dénes Petz Pdf

Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.

Author : Charles R. Johnson
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 53,9 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821801543

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Matrix Theory and Applications by Charles R. Johnson Pdf

This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

Author : Bernd Lohmann
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 40,9 Mb
Release : 2008-09-18
Category : Science
ISBN : 9783540746300

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Angle and Spin Resolved Auger Emission by Bernd Lohmann Pdf

Angle and spin resolved Auger emission physics deals with the theoretical and numerical description, analysis and interpretation of such types of experiments on free atoms and molecules. This monograph derives the general theory applying the density matrix formalism and, in terms of irreducible tensorial sets, so called state multipoles and order parameters, for parameterizing the atomic and molecular systems, respectively. It is the first book on angle and spin-resolved Auger emission.

Author : Xavier Oriols Pladevall,Jordi Mompart
Publisher : CRC Press
Page : 361 pages
File Size : 48,8 Mb
Release : 2019-05-24
Category : Science
ISBN : 9781000650563

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Applied Bohmian Mechanics by Xavier Oriols Pladevall,Jordi Mompart Pdf

Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schrödinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schrödinger equation, can be developed from it.

Author : Ángel S. Sanz,Salvador Miret-Artés
Publisher : Springer
Page : 333 pages
File Size : 45,6 Mb
Release : 2013-09-13
Category : Science
ISBN : 9783642179747

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A Trajectory Description of Quantum Processes. II. Applications by Ángel S. Sanz,Salvador Miret-Artés Pdf

Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.

Author : László Erdős,Horng-Tzer Yau
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 55,9 Mb
Release : 2017-08-30
Category : Random matrices
ISBN : 9781470436483

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A Dynamical Approach to Random Matrix Theory by László Erdős,Horng-Tzer Yau Pdf

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Author : Leticia González,Roland Lindh
Publisher : John Wiley & Sons
Page : 52 pages
File Size : 53,5 Mb
Release : 2021-02-01
Category : Science
ISBN : 9781119417750

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Quantum Chemistry and Dynamics of Excited States by Leticia González,Roland Lindh Pdf

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.