Kooperativer Bibliotheksverbund

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Format: XVII, 468 p. 1 illus. , online resource.

Edition: 1st ed. 2022.

ISBN: 9783031095481

Series Statement: Lecture Notes in Physics, 1003

Content: This book introduces and critically appraises the main proposals for how to understand quantum mechanics, namely the Copenhagen interpretation, spontaneous collapse, Bohmian mechanics, many-worlds, and others. The author makes clear what are the crucial problems, such as the measurement problem, related to the foundations of quantum mechanics and explains the key arguments like the Einstein-Podolsky-Rosen argument and Bell's proof of nonlocality. He discusses and clarifies numerous topics that have puzzled the founding fathers of quantum mechanics and present-day students alike, such as the possibility of hidden variables, the collapse of the wave function, time-of-arrival measurements, explanations of the symmetrization postulate for identical particles, or the nature of spin. Several chapters are devoted to extending the different approaches to relativistic space-time and quantum field theory. The book is self-contained and is intended for graduate students and researchers who want to step into the fundamental aspects of quantum physics. Given its clarity, it is accessible also to advanced undergraduates and contains many exercises and examples to master the subject.

Note: Waves and Particles -- Some Observables -- Collapse and Measurement -- Nonlocality -- General Observables -- Particle Creation -- Relativity -- Further Morals -- Appendix.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031095474

Additional Edition: Printed edition: ISBN 9783031095498

Language: English

Subjects: Physics

DOI: 10.1007/978-3-031-09548-1

URL: https://doi.org/10.1007/978-3-031-09548-1

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

UID:

Format: 1 online resource (478 pages)

ISBN: 9783031095481

Series Statement: Lecture notes in physics

Note: Intro -- Preface -- Contents -- Acronyms -- 1 Waves and Particles -- 1.1 Overview -- 1.2 The Schrödinger Equation -- 1.3 Unitary Operators in Hilbert Space -- 1.3.1 Existence and Uniqueness of Solutions of the Schrödinger Equation -- 1.3.2 The Time Evolution Operators -- 1.3.3 Unitary Matrices and Rotations -- 1.3.4 Inner Product -- 1.3.5 Abstract Hilbert Space -- 1.4 Classical Mechanics -- 1.4.1 Definition of Newtonian Mechanics -- 1.4.2 Properties of Newtonian Mechanics -- 1.4.3 Hamiltonian Systems -- 1.5 The Double-Slit Experiment -- 1.5.1 Classical Predictions for Particles and Waves -- 1.5.2 Actual Outcome of the Experiment -- 1.5.3 Feynman's Discussion -- 1.6 Bohmian Mechanics -- 1.6.1 Definition of Bohmian Mechanics -- 1.6.2 Properties of Bohmian Mechanics -- 1.6.3 Historical Overview -- 1.6.4 Equivariance -- 1.6.5 The Double-Slit Experiment in Bohmian Mechanics -- 1.6.6 Delayed-Choice Experiments -- Afshar's Experiment -- Exercises -- References -- 2 Some Observables -- 2.1 Fourier Transform and Momentum -- 2.1.1 Fourier Transform -- 2.1.2 Momentum -- 2.1.3 Momentum Operator -- 2.1.4 Tunnel Effect -- 2.1.5 External Magnetic Field -- 2.2 Operators and Observables -- 2.2.1 Heisenberg's Uncertainty Relation -- 2.2.2 Limitation to Knowledge -- 2.2.3 Self-Adjoint Operators -- 2.2.4 The Spectral Theorem -- 2.2.5 Born's Rule -- 2.2.6 Conservation Laws in Quantum Mechanics -- 2.2.7 The Dirac Delta Function -- 2.3 Spin -- 2.3.1 Spinors and Pauli Matrices -- 2.3.2 The Pauli Equation -- 2.3.3 The Stern-Gerlach Experiment -- 2.3.4 Bohmian Mechanics with Spin -- 2.3.5 Is an Electron a Spinning Ball? -- 2.3.6 Are There Actual Spin Values? -- 2.3.7 Many-Particle Systems -- 2.3.8 Representations of SO(3) -- 2.3.9 Inverted Stern-Gerlach Magnet and Contextuality -- Exercises -- References -- 3 Collapse and Measurement -- 3.1 The Projection Postulate. , 3.1.1 Notation -- 3.1.2 The Projection Postulate -- 3.1.3 Projection and Eigenspace -- 3.1.4 Position Measurements -- 3.1.5 Consecutive Quantum Measurements -- 3.2 The Measurement Problem -- 3.2.1 What the Problem Is -- 3.2.2 How Bohmian Mechanics Solves the Problem -- 3.2.3 Decoherence -- 3.2.4 Schrödinger's Cat -- 3.2.5 Positivism and Realism -- 3.2.6 Experiments and Operators -- 3.3 The GRW Theory -- 3.3.1 The Poisson Process -- 3.3.2 Definition of the GRW Process -- 3.3.3 Definition of the GRW Process in Formulas -- 3.3.4 Primitive Ontology -- 3.3.5 How GRW Theory Solves the Measurement Problem -- 3.3.6 Empirical Tests -- 3.3.7 The Need for a Primitive Ontology -- 3.4 The Copenhagen Interpretation -- 3.4.1 Two Realms -- 3.4.2 Elements of the Copenhagen View -- Positivism -- Purported Impossibility of Non-paradoxical Theories -- Completeness of the Wave Function -- Language of Measurement -- Narratives, But No Serious Ones -- 3.4.3 Complementarity -- 3.4.4 Reactions to the Measurement Problem -- 3.4.5 The Transactional Interpretation -- 3.5 Many Worlds -- 3.5.1 Schrödinger's Many-Worlds Theory -- 3.5.2 Everett's Many-Worlds Theory -- 3.5.3 Bell's First Many-Worlds Theory -- 3.5.4 Bell's Second Many-Worlds Theory -- 3.5.5 Probabilities in Many-Worlds Theories -- 3.6 Some Morals -- 3.7 Special Topics -- 3.7.1 Einstein's View -- 3.7.2 The Mach-Zehnder Interferometer -- 3.7.3 Path Integrals -- 3.7.4 Boundary Conditions -- 3.7.5 Point Interaction -- 3.7.6 No-Cloning Theorem -- 3.7.7 Aharonov-Bergmann-Lebowitz TimeReversal Symmetry -- Exercises -- References -- 4 Nonlocality -- 4.1 The Einstein-Podolsky-Rosen Argument -- 4.1.1 The EPR Argument -- 4.1.2 Square-Integrable Version -- 4.1.3 Further Conclusions -- 4.1.4 Bohm's Version of the EPR Argument Using Spin -- 4.1.5 Einstein's Boxes Argument -- 4.1.6 Too Good to Be True -- 4.2 Proof of Nonlocality. , 4.2.1 Bell's Experiment -- 4.2.2 Bell's 1964 Proof of Nonlocality -- 4.2.3 Bell's 1976 Proof of Nonlocality -- 4.3 Discussion of Nonlocality -- 4.3.1 Nonlocality in Bohmian Mechanics, GRW, Copenhagen, and Many-Worlds -- 4.3.2 Popular Myths About Bell's Theorem -- 4.3.3 Simultaneous Quantum Measurements -- 4.4 Special Topics -- 4.4.1 Bohr's Reply to EPR -- 4.4.2 The Frauchiger-Renner Paradox -- Exercises -- References -- 5 General Observables -- 5.1 POVMs: General Observables -- 5.1.1 Definition -- 5.1.2 The Main Theorem About POVMs -- 5.1.3 Limitations to Knowledge -- 5.1.4 Limitations to Knowledge as a General Fact -- 5.1.5 Limitations to Knowledge in Theories We Know -- 5.1.6 The Concept of Observable -- 5.2 Time of Detection -- 5.2.1 The Problem -- 5.2.2 The Quantum Zeno Effect -- 5.2.3 Allcock's Paradox -- 5.2.4 The Absorbing Boundary Rule -- 5.2.5 Time-Energy Uncertainty Relation -- 5.2.6 Historical Notes -- 5.3 Ontic Versus Epistemic -- 5.3.1 The Pusey-Barrett-Rudolph Theorem -- 5.4 Density Matrix and Mixed State -- 5.4.1 Trace -- 5.4.2 The Trace Formula in Quantum Mechanics -- 5.4.3 Pure and Mixed States -- 5.4.4 Empirically Equivalent Distributions -- 5.4.5 Density Matrix and Dynamics -- 5.5 Reduced Density Matrix and Partial Trace -- 5.5.1 Tensor Product -- 5.5.2 Definition of the Reduced Density Matrix -- 5.5.3 Partial Trace -- 5.5.4 The Trace Formula Again -- 5.5.5 The Measurement Problem and Density Matrices -- 5.5.6 POVM and Collapse -- 5.5.7 Completely Positive Superoperators -- 5.5.8 The Main Theorem About Superoperators -- 5.5.9 The No-Signaling Theorem -- 5.5.10 Canonical Typicality -- 5.5.11 The Possibility of a Fundamental Density Matrix -- 5.6 Quantum Logic -- 5.6.1 Boolean Algebras -- 5.6.2 Quantum Measures -- 5.7 No-Hidden-Variables Theorems -- 5.7.1 Bell's NHVT -- 5.7.2 Von Neumann's NHVT -- 5.7.3 Gleason's NHVT. , 5.7.4 Hidden Variables and Ontology -- 5.8 Special Topics -- 5.8.1 The Decoherent Histories Interpretation -- 5.8.2 The Hilbert-Schmidt Inner Product -- Exercises -- References -- 6 Particle Creation -- 6.1 Identical Particles -- 6.1.1 Symmetrization Postulate -- 6.1.2 Schrödinger Equation and Symmetry -- 6.1.3 The Space of Unordered Configurations -- 6.1.4 Identical Particles in Bohmian Mechanics -- 6.1.5 Identical Particles in GRW Theory -- 6.2 Hamiltonians of Particle Creation -- 6.2.1 Configuration Space of a Variable Number of Particles -- 6.2.2 Fock Space -- The Fock Space of Spinless Bosons -- The Fock Space of Spinless Fermions -- General Fock Space -- Two Species -- 6.2.3 Example: Emission-Absorption Model -- 6.2.4 Creation and Annihilation Operators -- 6.2.5 Ultraviolet Divergence -- 6.3 Particle Creation as Such -- 6.3.1 Jumps -- 6.3.2 Bell's Jump Process -- 6.3.3 Virtual Particles -- 6.3.4 GRW Theory and Many-Worlds in Fock Space -- 6.4 Interior-Boundary Conditions -- 6.4.1 What an IBC Is -- 6.4.2 Configuration Space with Two Sectors -- Hilbert Space -- Spherical Coordinates -- Probability Transport -- Hamiltonian and IBC -- Delta Contribution -- 6.4.3 All Sectors -- Hamiltonian -- Jump Process -- Ground State -- 6.5 A Brief Look at Quantum Field Theory -- 6.5.1 Problems of Quantum Field Theory -- 6.5.2 Field Ontology vs. Particle Ontology -- Exercises -- References -- 7 Relativity -- 7.1 Brief Introduction to Relativity -- 7.1.1 Galilean Relativity -- 7.1.2 Minkowski Space -- 7.1.3 Dual Space -- 7.1.4 Arc Length -- 7.1.5 Index Contraction -- 7.1.6 Classical Electrodynamics as a Paradigm of a Relativistic Theory -- 7.1.7 Cauchy Surfaces -- 7.1.8 Outlook on General Relativity -- 7.2 Relativistic Schrödinger Equations -- 7.2.1 The Klein-Gordon Equation -- Fourier Transform -- Dispersion Relation -- The Klein-Gordon Equation. , Positive Energy Solutions -- 7.2.2 Two-Spinors and Four-Vectors -- Two-Spinors and Three-Vectors -- Action of Lorentz Transformations -- Conjugate Vector Space -- Relation to 4-Vectors -- Lorentz-Invariant Product -- 7.2.3 The Weyl Equation -- Relation to the Klein-Gordon Equation -- 7.2.4 The Dirac Equation -- Relation to the Klein-Gordon Equation -- Lorentz Invariance -- 7.3 Probability -- 7.3.1 Current for the Weyl Equation -- 7.3.2 Current for the Dirac Equation -- 7.3.3 Probability Flow -- Equation of Motion -- Surface Equivariance -- 7.3.4 Evolution Between Cauchy Surfaces -- 7.3.5 Propagation Locality -- 7.3.6 External Fields -- 7.3.7 Non-Relativistic Limit -- 7.3.8 Probability and the Klein-Gordon Equation -- Psi Squared -- The Klein-Gordon Current -- 7.3.9 The Maxwell Equation as the Schrödinger Equation for Photons -- Locally Plane Waves -- The Poynting Vector -- One Over Root omega -- The Kappa Operator -- Desiderata -- 7.4 Many Particles -- 7.4.1 Multi-Time Wave Functions -- 7.4.2 Surface Wave Functions -- 7.5 Which Theories Count as Relativistic? -- 7.5.1 Lorentz Invariance -- 7.5.2 Other Relativistic Properties -- 7.5.3 Relativistic Quantum Theories Without Observers -- 7.5.4 The Time Foliation -- 7.6 Bohmian Mechanics in Relativistic Space-Time -- 7.6.1 Law of Motion -- 7.6.2 Equivariance -- Intersection Probability and Detection Probability -- No Signaling -- 7.6.3 The Spin-0 Case -- Definition of the Current Tensor -- Trajectories -- Time Travel -- 7.7 Predictions in Relativistic Space-Time -- 7.7.1 Is Collapse Compatible with Relativity? -- The Aharonov-Albert Wave Function -- Other Approaches to Relativistic Collapse -- 7.7.2 Tunneling Speed -- 7.8 GRW Theory in Relativistic Space-Time -- 7.8.1 1-Particle Case -- Ingredients -- Definition -- POVM -- 7.8.2 The Case of N Non-Interacting Particles -- Definition -- Properties. , Collapsed Wave Function.

Additional Edition: Print version: Tumulka, Roderich Foundations of Quantum Mechanics Cham : Springer International Publishing AG,c2022 ISBN 9783031095474

Language: English