The Formalisms Of Quantum Mechanics

Author : Francois David
Publisher : Springer
Page : 157 pages
File Size : 40,6 Mb
Release : 2014-11-06
Category : Science
ISBN : 9783319105390

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The Formalisms of Quantum Mechanics by Francois David Pdf

These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics.

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 42,8 Mb
Release : 2009-05-21
Category : Science
ISBN : 9781402095931

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Contextual Approach to Quantum Formalism by Andrei Y. Khrennikov Pdf

The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.

Author : Roy McWeeny
Publisher : Courier Corporation
Page : 176 pages
File Size : 43,7 Mb
Release : 2012-05-23
Category : Science
ISBN : 9780486143804

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Quantum Mechanics by Roy McWeeny Pdf

Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.

Author : Tilak Sinha
Publisher : CRC Press
Page : 267 pages
File Size : 55,5 Mb
Release : 2021-08-19
Category : Science
ISBN : 9781000415636

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An Introduction to Quantum Mechanics by Tilak Sinha Pdf

Demonstrates why linear algebra is the appropriate mathematical language for quantum mechanics. Uses a reconstructive approach to motivate the postulates of quantum mechanics. Builds the vocabulary of quantum mechanics by showing how the entire body of its conceptual ingredients can be constructed from the single notion of quantum measurement.

Author : K. Kong Wan
Publisher : CRC Press
Page : 720 pages
File Size : 50,9 Mb
Release : 2019-07-09
Category : Science
ISBN : 9781351333368

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Quantum Mechanics by K. Kong Wan Pdf

The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning, which makes it difficult to appreciate the mathematical formalism and understand quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. This book is divided into four parts. Part I is a brief review of the general properties of classical and quantum systems. A general discussion of probability theory is also included which aims to help in understanding the probability theories relevant to quantum mechanics. Part II is a detailed study of the mathematics for quantum mechanics. Part III presents quantum mechanics in a series of postulates. Six groups of postulates are presented to describe orthodox quantum systems. Each statement of a postulate is supplemented with a detailed discussion. To make them easier to understand, the postulates for discrete observables are presented before those for continuous observables. Part IV presents several illustrative applications, which include harmonic and isotropic oscillators, charged particle in external magnetic fields and the Aharonov–Bohm effect. For easy reference, definitions, theorems, examples, comments, properties and results are labelled with section numbers. Various symbols and notations are adopted to distinguish different quantities explicitly and to avoid misrepresentation. Self-contained both mathematically and physically, the book is accessible to a wide readership, including astrophysicists, mathematicians and philosophers of science who are interested in the foundations of quantum mechanics.

Author : Pavel Mnev
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 40,6 Mb
Release : 2019-08-20
Category : Algebras, Linear
ISBN : 9781470452711

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Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications by Pavel Mnev Pdf

This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.

Author : Carlos Navarrete-Benlloch
Publisher : Morgan & Claypool Publishers
Page : 93 pages
File Size : 41,8 Mb
Release : 2016-01-01
Category : Science
ISBN : 9781681744063

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An Introduction to the Formalism of Quantum Information with Continuous Variables by Carlos Navarrete-Benlloch Pdf

Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.

Author : Giampiero Esposito,Giuseppe Marmo,George Sudarshan
Publisher : Cambridge University Press
Page : 612 pages
File Size : 51,7 Mb
Release : 2004-03-11
Category : Science
ISBN : 9781139450546

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From Classical to Quantum Mechanics by Giampiero Esposito,Giuseppe Marmo,George Sudarshan Pdf

This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.

Author : Travis Norsen
Publisher : Springer
Page : 310 pages
File Size : 51,7 Mb
Release : 2017-08-17
Category : Science
ISBN : 9783319658674

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Foundations of Quantum Mechanics by Travis Norsen Pdf

Authored by an acclaimed teacher of quantum physics and philosophy, this textbook pays special attention to the aspects that many courses sweep under the carpet. Traditional courses in quantum mechanics teach students how to use the quantum formalism to make calculations. But even the best students - indeed, especially the best students - emerge rather confused about what, exactly, the theory says is going on, physically, in microscopic systems. This supplementary textbook is designed to help such students understand that they are not alone in their confusions (luminaries such as Albert Einstein, Erwin Schroedinger, and John Stewart Bell having shared them), to sharpen their understanding of the most important difficulties associated with interpreting quantum theory in a realistic manner, and to introduce them to the most promising attempts to formulate the theory in a way that is physically clear and coherent. The text is accessible to students with at least one semester of prior exposure to quantum (or "modern") physics and includes over a hundred engaging end-of-chapter "Projects" that make the book suitable for either a traditional classroom or for self-study.

Author : K. Kong Wan
Publisher : World Scientific
Page : 712 pages
File Size : 50,5 Mb
Release : 2006
Category : Science
ISBN : 9781860946257

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From Micro to Macro Quantum Systems by K. Kong Wan Pdf

Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations.This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schr”dinger's cat states in superconducting systems, and a path space formulation of quantum mechanics.This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators.

Author : Bryce S. DeWitt
Publisher : Unknown
Page : 294 pages
File Size : 54,6 Mb
Release : 1955
Category : Electronic
ISBN : UOM:39015077590290

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The Operator Formalism in Quantum Perturbation Theory by Bryce S. DeWitt Pdf

Author : Gonzalo Muga,R. Sala Mayato,Inigo Egusquiza
Publisher : Springer
Page : 455 pages
File Size : 55,9 Mb
Release : 2007-11-30
Category : Science
ISBN : 9783540734734

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Time in Quantum Mechanics by Gonzalo Muga,R. Sala Mayato,Inigo Egusquiza Pdf

The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the quantum theory. This multi-authored book, written as an introductory guide for newcomers to the subject, as well as a useful source of information for the expert, covers many of the open questions. The book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory.

Author : W.M. de Muynck
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 47,9 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306480478

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Foundations of Quantum Mechanics, an Empiricist Approach by W.M. de Muynck Pdf

Taking a new perspective provided by a generalization of the mathematical formalism encompassing positive operator-valued measures, this book views old and new problems of the foundations of quantum mechanics. It demonstrates the crucial role of the generalized formalism in fundamental issues and practical applications.

Author : Roy MacWeeny
Publisher : Unknown
Page : 155 pages
File Size : 46,7 Mb
Release : 2003
Category : Electronic
ISBN : OCLC:630216310

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Quantum Mechanics by Roy MacWeeny Pdf

Author : Gerrit Coddens
Publisher : World Scientific
Page : 404 pages
File Size : 45,6 Mb
Release : 2015-06-29
Category : Science
ISBN : 9781783266395

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From Spinors To Quantum Mechanics by Gerrit Coddens Pdf

From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics.In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible.