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International School of Physics 'Enrico Fermi' ;.
Foundations of quantum theory. — Course 197. / edited by E.M. Rasel and W.P. Schleich. — 1 online resource. — (International School of Physics 'Enrico Fermi'). — <URL:http://elib.fa.ru/ebsco/2030796.pdf>.

Record create date: 2/20/2019

Subject: Quantum theory.; SCIENCE / Energy.; SCIENCE / Mechanics / General.; SCIENCE / Physics / General.

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Table of Contents

  • Title Page
  • Contents
  • Preface
  • Course group shot
  • Science in tumultuous times
    • Introduction
    • 1. The years of the First World War (1914-1918)
    • 2. Post-War years (1919-1921)
    • 3. Quantum mechanics (the 1920s)
    • 4. Exile (1933)
    • 5. The atom bomb (1945)
    • 6. The Nobel Prize (1954)
    • 7. Conclusion (1970)
    • Appendix A
    • Appendix B
  • But God does play dice: The path to quantum mechanics
    • Introduction
    • 1. Breslau, Germany (now Wroclaw, Poland)
    • 2. Gottingen
    • 3. Frankfurt
    • 4. Gottingen again
    • 5. America
    • 6. Gottingen
  • From the Bohr model to Heisenberg's quantum mechanics
    • 1. Introduction
    • 2. From Balmer to Bohr
    • 3. The Bohr model between success and failure
    • 4. Heisenberg's path from classical physics to quantum mechanics
      • 4.1. Action integral in Fourier space
      • 4.2. Extension to an arbitrary frequency spectrum
      • 4.3. The appearance of non-commuting quantities
    • 5. Quantization of the linear harmonic oscillator
    • 6. Light at the end of the tunnel
  • The linearity of quantum mechanics and the birth of the Schrodinger equation
    • 1. Introduction
      • 1.1. Linearization of the non-linear wave equation
      • 1.2. Key ideas of our previous approaches
      • 1.3. Outline
    • 2. Road towards the Schrodinger equation
    • 3. Comparison with the literature
    • 4. Why zero?
      • 4.1. A curious mathematical identity
      • 4.2. Definition of a quantum wave by its amplitude
      • 4.3. Formulation of the problem
    • 5. Classical mechanics guides the amplitude of the Schrodinger wave
      • 5.1. Hamilton-Jacobi theory in a nutshell
      • 5.2. Classical action as a phase field
    • 6. Quantum condition implies linear Schrodinger equation
      • 6.1. Emergence of a quantum phase
      • 6.2. Continuity equation with quantum current
      • 6.3. Quantum Hamilton-Jacobi equation
    • 7. Classicality condition implies non-linear wave equation
      • 7.1. General real amplitude
      • 7.2. Amplitude given by Van Vleck determinant
        • 7.2.1. Super-classical waves
        • 7.2.2. Super-classical waves are WKB waves
    • 8. From Van Vleck via Rosen to Schrodinger
      • 8.1. The need for linearity
      • 8.2. Linearization due to quantum current
    • 9. Summary and outlook
    • Appendix A. Van Vleck continuity equation
      • Appendix A.1. One-dimensional case
        • Appendix A.1.1. Derivation of continuity equation
        • Appendix A.1.2. Explicit expressions for density and current from action
        • Appendix A.1.3. Density and current from continuity equation
      • Appendix A.2. Multi-dimensional case
      • Appendix A.3. Differential of a determinant
    • Appendix B. Non-linear wave equation for WKB wave
  • Wave phenomena and wave equations
    • 1. Preludium
    • 2. Water waves
      • 2.1. Wave equation for water waves
    • 3. Matter wave
      • 3.1. Wave equation for matter wave
    • 4. Final remark
    • 5. Further readings
  • History leading to Bell's inequality and experiments
    • 1. Introduction
    • 2. Early history
    • 3. The beginnings of quantum mechanics
    • 4. Bell Inequalities
    • 5. Initial experiments
  • Sewing Greenberger-Horne-Zeilinger states with a quantum zipper
    • 1. Introduction
    • 2. Mechanism
    • 3. Implementation
  • Quantum state generation via frequency combs
    • 1. Optical quantum state preparation
    • 2. Quantum frequency combs from bulk-based systems
    • 3. Integrated quantum frequency combs
    • 4. Conclusion
  • Time after time: From EPR to Wigner's friend and quantum eraser
    • 1. Introduction
    • 2. The Einstein-Podolsky-Rosen (EPR) problem
    • 3. Of Wigner and Wigner's friends
    • 4. Quantum eraser and the Mohrhoff conundrum
    • 5. Summary
  • QBism: Quantum theory as a hero's handbook
    • 1. Introduction
    • 2. Exactly how quantum states fail to exist
    • 3. Teleportation
    • 4. The meaning of no-cloning
    • 5. The essence of Bell's theorem, QBism style
    • 6. The quantum de Finetti theorem
    • 7. Seeking SICs - The Born rule as fundamental
    • 8. Mathematical intermezzo: The sporadic SICs
    • 9. Hilbert-space dimension as a universal capacity
    • 10. Quantum cosmology from the inside
    • 11. The future
  • Information-theoretic derivation of free quantum field theory
    • 1. Introduction
    • 2. Derivation from principles of the quantum-walk theory
      • 2.1. The quantum system: qubit, fermion or boson?
      • 2.2. Quantum walks on Cayley graphs
        • 2.2.1. The homogeneity principle
        • 2.2.2. The locality principle
        • 2.2.3. The isotropy principle
        • 2.2.4. The unitarity principle
      • 2.3. Restriction to Euclidean emergent space
        • 2.3.1. Geometric group theory
    • 3. Quantum walks on Abelian groups and free QFT as their relativistic regime
      • 3.1. Induced representation, and reduction from virtually-Abelian to Abelian quantum walks
      • 3.2. Isotropy and orthogonal embedding in R3
      • 3.3. Quantum walks with Abelian G
      • 3.4. Dispersion relation
      • 3.5. The relativistic regime
      • 3.6. Schrodinger equation for the ultra-relativistic regime
      • 3.7. Recovering the Weyl equation
      • 3.8. Recovering the Dirac equation
        • 3.8.1. Discriminability between quantum walk and quantum field dynamics
        • 3.8.2. Mass and proper-time
        • 3.8.3. Physical dimensions and scales for mass and discreteness
      • 3.9. Recovering Maxwell fields
        • 3.9.1. Photons made of pairs of fermions
        • 3.9.2. Vacuum dispersion
    • 4. Recovering special relativity in a discrete quantum universe
      • 4.1. Quantum-digital Poincare group and the notion of particle
      • 4.2. De Sitter group for non-vanishing mass
    • 5. Conclusions and future perspectives: the interacting theory, ..., gravity?
  • Revealing quantum properties with simple measurements
    • 1. Introduction
    • 2. Wave-particle duality
      • 2.1. Wave-particle duality: an inequality
        • 2.1.1. Distinguishability
        • 2.1.2. Visibility
        • 2.1.3. The wave-particle inequality
      • 2.2. Simultaneous measurements
      • 2.3. Higher-order wave-particle duality
        • 2.3.1. Higher-order distinguishability
        • 2.3.2. Higher-order visibility
        • 2.3.3. Higher-order wave-particle duality
      • 2.4. Duality and entanglement
    • 3. Entanglement
      • 3.1. Bipartite entanglement
        • 3.1.1. Schmidt decomposition
        • 3.1.2. The positive partial transpose criterion
        • 3.1.3. Detecting entanglement with the help of the Cauchy-Schwarz inequality
      • 3.2. Tripartite entanglement
      • 3.3. Multipartite entanglement
      • 3.4. The spatial distribution of entanglement
    • 4. Conclusion
    • Appendix A. Proof of eq. (49)
  • Complementarity and light modes
    • 1. Introduction
    • 2. Spontaneous parametric down-conversion (SPDC) as a tool
    • 3. Induced coherence in the 3-crystal set up
    • 4. Stimulated coherence
    • 5. Complementarity in the spatial dimension
    • 6. Complementarity for single photons in higher-order spatial modes
    • 7. Conclusion
  • Quantum imaging
    • 1. What is quantum imaging?
    • 2. Brief history of quantum methods in metrology
    • 3. Parametric downconversion and the generation of entangled photons
    • 4. What is ghost imaging and what are its properties?
    • 5. Interaction-free imaging
    • 6. Imaging by Mandel's induced coherence
    • 7. Technology for quantum imaging
    • 8. Summary and discussion
  • Spekkens' toy model and contextuality as a resource in quantum computation
    • 1. Spekkens' toy model
    • 2. Contextuality
    • 3. Restricting SM as a subtheory of QM
  • Casimir forces in spherically symmetric dielectric media
    • 1. Introduction
    • The spherical problem
    • 2. Renormalization and Lifshitz theory
    • 3. Results
  • The strange roles of proper time and mass in physics
    • 1. Mass: The role it plays, and the role it ought to play
    • 2. Proper time: The role it plays, and the role it ought to play
    • 3. The equivalence principle and the extended equivalence principle
      • 3.1. Stable particles: The equivalence principle
      • 3.2. Unstable particles: The extended equivalence principle
    • 4. Incorporating mass and proper time as dynamical variables
    • 5. An extended Lorentz transformation and Schrodinger equation
  • Some consequences of mass and proper time as dynamical variables
    • 1. The Lorentz transformation and the Galilean transformation
      • 1.1. The Bargmann theorem in non-relativistic physics
      • 1.2. The problem with the Bargmann theorem
    • 2. The mass-proper time uncertainty relation
    • 3. The classical limit of the equivalence principle
      • 3.1. The strange mass scaling in phase space
    • 4. The different correspondence principles for gravity and non-gravity forces: matrix elements in the classical limit
  • Atom interferometry and its applications
    • 1. Introduction
      • 1.1. Applications of atom interferometry
      • 1.2. Optical elements for atoms
      • 1.3. Sources for atom optics
      • 1.4. Overview
    • 2. Tools of atom interferometry
      • 2.1. Beam splitters and mirrors
        • 2.1.1. Rabi oscillations and two-photon coupling
        • 2.1.2. Bragg and Raman diffraction
        • 2.1.3. Multi-photon coupling by Bragg diffraction
        • 2.1.4. Influence of atom cloud and beam size
      • 2.2. Optical lattices
        • 2.2.1. Bloch theorem
        • 2.2.2. Bloch oscillations
        • 2.2.3. Landau-Zener transitions
      • 2.3. Mach-Zehnder interferometer for gravity measurements
        • 2.3.1. Set-up
        • 2.3.2. Contributions to phase shift
        • 2.3.3. Influence of non-zero pulse duration
        • 2.3.4. Measurement of gravitational acceleration
    • 3. Equivalence principle and atom interferometry
      • 3.1. Frameworks for tests of the universality of free fall
      • 3.2. Simultaneous 87Rb and 39K interferometer
      • 3.3. Data analysis and result
    • 4. Atom-chip-based BEC interferometry
      • 4.1. Delta-kick collimation
      • 4.2. Quantum tiltmeter based on double Bragg diffraction
        • 4.2.1. Rabi oscillations
        • 4.2.2. Tilt measurements
      • 4.3. Sensitive atom-chip gravimeter on a compact baseline
        • 4.3.1. Relaunch of atoms in a retro-reflected optical lattice
        • 4.3.2. Experimental sequence of the atom-chip gravimeter
        • 4.3.3. Analysis of the interferometer output
    • 5. Outlook
      • 5.1. Reduced systematic uncertainties in future devices
      • 5.2. Very long baseline atom interferometry
      • 5.3. Space-borne atom interferometers
  • Atom-chip-based quantum gravimetry with BECs
    • 1. Introduction
    • 2. Atom-chip-based gravimeter prototype in QUANTUS-1
    • 3. Next generation quantum gravimeter QG-1 for mobile applications
  • Gravitational properties of light
  • List of participants

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