Foundations of quantum mechanics / / Roderich Tumulka

• Autore: Tumulka Roderich
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (478 pages)
• Disciplina: 530.12
• Soggetto topico: Quantum theory
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Titolo autorizzato: Foundations of Quantum Mechanics
• ISBN: 9783031095481; 9783031095474
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910632483103321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture notes in physics.