The Formalisms of Quantum Mechanics

The Formalisms of Quantum Mechanics

This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics.

Author: Francois David

Publisher: Springer

ISBN: 9783319105390

Category: Science

Page: 157

View: 517

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.
Categories: Science

An Introduction to Quantum Mechanics

An Introduction to Quantum Mechanics

This book strives to underline this as strongly as possible. The book is intended as an undergraduate text for a first course in quantum mechanics.

Author: Tilak Sinha

Publisher: CRC Press

ISBN: 9781000415636

Category: Science

Page: 266

View: 404

The core content of even the most intricate intellectual edifices is often a simple fact or idea. So is it with quantum mechanics; the entire mathematical fabric of the formal description of quantum mechanics stems essentially from the fact that quantum probabilities interfere (i.e., from the superposition principle). This book is dedicated to substantiating this claim. In the process, the book tries to demonstrate how the factual content of quantum mechanics can be transcribed in the formal language of vector spaces and linear transformations by disentangling the empirical content from the usual formal description. More importantly, it tries to bring out what this transcription achieves. The book uses a pedagogic strategy which reverse engineers the postulates of quantum mechanics to device a schematic outline of the empirical content of quantum mechanics from which the postulates are then reconstructed step by step. This strategy is adopted to avoid the disconcerting details of actual experiments (however simplified) to spare the beginner of issues that lurk in the fragile foundations of the subject. In the Copenhagen interpretation of quantum mechanics, the key idea is measurement. But "measurement" carries an entirely different meaning from the connotation that the term carries elsewhere in physics. This book strives to underline this as strongly as possible. The book is intended as an undergraduate text for a first course in quantum mechanics. Since the book is self contained, it may also be used by enthusiastic outsiders interested to get a glimpse of the core content of the subject. Features: 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.
Categories: Science

Introduction to Path integral Methods in Physics and Polymer Science

Introduction to Path integral Methods in Physics and Polymer Science

1 Quantum Theory of Many Variable Systems and Fields by B Sakita ( CUNY ) These lecture notes evolved from special courses on ... Contents : Canonical Operator Formalism of Quantum Mechanics ; Path - Integral Formalism ; Path - Integral ...

Author: Frederik W. Wiegel

Publisher: World Scientific

ISBN: 9971978709

Category: Science

Page: 197

View: 629

This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
Categories: Science

From Micro to Macro Quantum Systems

From Micro to Macro Quantum Systems

Introduction to Aaciomatic Quantum Field Theory, Benjamin, Reading, Mass. Böhm, A. (1978). The Rigged Hilbert Space and Quantum Mechanics (Lecture Notes in Physics 78), Springer-Verlag, Berlin. Böhm, A. (1979), Quantum Mechanics, ...

Author: K Kong Wan

Publisher: World Scientific

ISBN: 9781783260010

Category: Science

Page: 708

View: 255

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, Schrödinger'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. Contents:Aspects of Geometric and Operator Theories:Manifolds and Dynamical SystemsOperators and Their Direct IntegralsOrthodox and Generalized Quantum Mechanics:Orthodox Quantum MechanicsPhysical Theory in Hilbert SpaceGeneralized Quantum MechanicsPoint Interactions, Macroscopic Quantum Systems and Superselection Rules:Point InteractionsMacroscopic Quantum SystemsAsymptotic Disjointness, Asymptotic Separability, Quantum Mechanics on Path Space and Superselection Rules:Separability and DecoherenceQuantum Mechanics on Path Space Readership: Theoretical and mathematical physicists, applied and pure mathematicians, physicists and philosophers of science (with an interest in quantum theory). Key Features:Rigorous formulation of a unified theory in a form directly applicable to physical systemsIntroduction of a quantization-by-part scheme to treat point interactionsSystematic and explicit treatment of quantum circuits in terms of point interactionsDistinctive selection of materials rarely discussed elsewhere, including a large number of examples and contemporary topicsDiscussions on the interplay of mathematics and physicsKeywords:Quantum Mechanics;Quantization;Macroscopic Quantum Systems;Superconducting Circuits;Point Contact InteractionsReviews:“Numerous sections of the book can be studied (and are really worth studying) like a textbook and without the necessity of going through the rest of the volume … certainly, everyone who works through the book will be rewarded by an enhanced comprehension of orthodox quantum theory … there are many solid reasons for recommending this book to the whole community of physicists and mathematicians — from graduate students to researchers — interested in a fresh description of the microscopic and macroscopic quantum worlds.”Mathematical Reviews
Categories: Science

A First Introduction to Quantum Physics

A First Introduction to Quantum Physics

The following is a list of recommended reading for anyone who wants to learn quantum mechanics in more detail. ... part of Springer Nature 2018 P. Kok, A First Introduction to Quantum Physics, 231 Undergraduate Lecture Notes in Physics, ...

Author: Pieter Kok

Publisher: Springer

ISBN: 9783319922072

Category: Science

Page: 243

View: 573

In this undergraduate textbook, the author develops the quantum theory from first principles based on very simple experiments: a photon travelling through beam splitters to detectors, an electron moving through a Stern-Gerlach machine, and an atom emitting radiation. From the physical description of these experiments follows a natural mathematical description in terms of matrices and complex numbers. The first part of the book examines how experimental facts force us to let go of some deeply held preconceptions and develops this idea into a mathematical description of states, probabilities, observables, and time evolution using physical applications. The second part of the book explores more advanced topics, including the concept of entanglement, the process of decoherence, and extension of the quantum theory to the situation of a particle in a one-dimensional box. Here, the text makes contact with more traditional treatments of quantum mechanics. The remaining chapters delve deeply into the idea of uncertainty relations and explore what the quantum theory says about the nature of reality. The book is an ideal and accessible introduction to quantum physics, with modern examples and helpful end-of-chapter exercises.
Categories: Science

Lecture Notes on Quantum Mechanics

Lecture Notes on Quantum Mechanics

... of this book is to provide an introductory course in a fundamental and acedemically required subject , as well as fill a gap in the physics education of scientists , many of whom have either never formally studied quantum mechanics ...

Author: Samuel D. Lindenbaum

Publisher: World Scientific

ISBN: 9810238398

Category: Science

Page: 343

View: 978

The chapters are not independent, but build on one another. Subjects range from the failures of classical theory to second quantization, including chapters on the Dirac theory and Feynman diagrams."--Pub. desc.
Categories: Science

Quantum Mechanics for Pedestrians 1

Quantum Mechanics for Pedestrians 1

This revised second edition is expanded by an introduction to some ideas and problems of relativistic quantum mechanics. In this first volume, the Klein-Gordon and the Dirac equations are treated.

Author: Jochen Pade

Publisher: Springer

ISBN: 9783030004644

Category: Science

Page: 522

View: 806

This book, the first in a two-volume set, provides an introduction to the fundamentals of (mainly) non-relativistic quantum mechanics. This first volume chiefly focuses on the essential principles, while applications and extensions of the formalism can be found in volume 2. Including but also moving beyond material that is covered in traditional textbooks on quantum mechanics, the book discusses in detail current issues such as interaction-free quantum measurements or neutrino oscillations, as well as fundamental problems and epistemological questions, such as the measurement problem. A chapter on the postulates of quantum mechanics rounds off this first volume. In order to quickly and clearly present the main principles of quantum mechanics and its mathematical formulation, there is a systematic transition between wave mechanics and algebraic representation in the first few chapters, in which the required mathematical tools are introduced step by step. Moreover, the appendix concisely reviews the most important mathematical tools, allowing readers to largely dispense with supplementary literature. The appendix also explores advanced topics, such as the Quantum-Zeno effect and time-delay experiments. Over 250 exercises, most of them with solutions, help to deepen the reader’s understanding of the topics discussed. This revised second edition is expanded by an introduction to some ideas and problems of relativistic quantum mechanics. In this first volume, the Klein-Gordon and the Dirac equations are treated. Fundamentals of other areas are compiled in compact form, i.e., outlines of special relativity, classical field theory and electrodynamics. The book is chiefly intended for student science teachers and all students of physics, majors and minors alike, who are looking for a reasonably easy and modern introduction to quantum mechanics.
Categories: Science

Quantum Gravity

Quantum Gravity

This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity.

Author: Domenico J. W. Giulini

Publisher: Springer Science & Business Media

ISBN: 354040810X

Category: Science

Page: 426

View: 180

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.
Categories: Science

Time in Quantum Mechanics

Time in Quantum Mechanics

This novel monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics. For this revised second edition, all chapters have been updated and extended where appropriate.

Author: Gonzalo Muga

Publisher: Springer Science & Business Media

ISBN: 9783540734727

Category: Science

Page: 455

View: 468

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.
Categories: Science

An Introduction to Covariant Quantum Mechanics

An Introduction to Covariant Quantum Mechanics

C. Duval, The Dirac & Levy-Leblond equations and geometric quantization, in Differential Geometric Methods in Mathematical Physics, ed. by P.L. García, A. Pérez-Rendón, Lecture Notes in Math.

Author: Josef Janyška

Publisher: Springer Nature

ISBN: 9783030895891

Category:

Page:

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