Bohmian Mechanics. The Physics and Mathematics of Quantum Theory. Bearbeitet von Detlef Dürr, Stefan Teufel

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1 Bohmian Mechanics The Physics and Mathematics of Quantum Theory Bearbeitet von Detlef Dürr, Stefan Teufel 1. Auflage Buch. xii, 393 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 1650 g Weitere Fachgebiete > Physik, Astronomie > Quantenphysik Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents 1 Introduction Ontology: What There Is Extracts In Brief: The Problem of Quantum Mechanics In Brief: Bohmian Mechanics DeterminismandRealism... 9 References Classical Physics Newtonian Mechanics Hamiltonian Mechanics Hamilton Jacobi Formulation Fields and Particles: Electromagnetism No fields, Only Particles: Electromagnetism On the Symplectic Structure of the Phase Space References Symmetry Chance Typicality TypicalBehavior.TheLawofLargeNumbers Statistical Hypothesis and Its Justification Typicality in Subsystems: Microcanonical and Canonical Ensembles Irreversibility Typicality Within Atypicality OurAtypicalUniverse Ergodicity and Mixing Probability Theory Lebesgue Measure and Coarse-Graining ix

3 x Contents TheLawofLargeNumbers References Brownian motion Einstein sargument On Smoluchowski s Microscopic Derivation PathIntegration References The Beginning of Quantum Theory References Schrödinger s Equation TheEquation WhatPhysicsMustNotBe Interpretation, Incompleteness, and ρ = ψ References Bohmian Mechanics Derivation of Bohmian Mechanics Bohmian Mechanics and Typicality ElectronTrajectories Spin A Topological View of Indistinguishable Particles References The Macroscopic World PointerPositions EffectiveCollapse Centered Wave packets The Classical Limit of Bohmian Mechanics SomeFurtherObservations Dirac Formalism, Density Matrix, Reduced Density Matrix, and Decoherence Poincaré Recurrence References Nonlocality Singlet State and Probabilities for Anti-Correlations Faster Than Light Signals? References The Wave Function and Quantum Equilibrium Measure of Typicality Conditional Wave Function EffectiveWavefunction...216

4 Contents xi 11.4 TypicalEmpiricalDistributions Misunderstandings Quantum Nonequilibrium References From Physics to Mathematics Observables. An Unhelpful Notion WhoIsAfraidofPVMsandPOVMs? The Theory Decides What Is Measurable Joint Probabilities Naive Realism about Operators Schrödinger s Equation Revisited WhatComesNext? References Hilbert Space The Hilbert Space L The Coordinate Space l Fourier Transformation on L Bilinear Forms and Bounded Linear Operators Tensor Product Spaces References The Schrödinger Operator Unitary Groups and Their Generators Self-AdjointOperators The Atomistic Schrödinger Operator References Measures and Operators ExamplesofPVMsandTheirOperators Heisenberg Operators Asymptotic Velocity and the Momentum Operator The Spectral Theorem TheDiracFormalism Mathematics of the Spectral Theorem Spectral Representations Unbounded Operators Unitary Groups H 0 = Δ/ The Spectrum References...344

5 xii Contents 16 Bohmian Mechanics on Scattering Theory ExitStatistics AsymptoticExits Scattering Theory and Exit Distribution More on Abstract Scattering Theory Generalized Eigenfunctions TowardstheScatteringCross-Section TheScatteringCross-Section Born sformula Time-Dependent Scattering References Epilogue References Bibliography Index...387