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Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics : with critical notes of the author

Author: Louis de Broglie
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers, ©1990.
Series: Fundamental theories of physics, v. 40.
Edition/Format:   Book : EnglishView all editions and formats

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Document Type: Book
All Authors / Contributors: Louis de Broglie
ISBN: 0792309294 9780792309291
OCLC Number: 22494715
Notes: Translation of: Les incertitudes d'Heisenberg et l'interprétation probabiliste de la mécanique ondulatoire.
Description: xliv, 302 pages : illustrations ; 25 cm.
Contents: One (1950-1951) On Heisenberg's Uncertainties and the Probabilistic Interpretation of Wave Mechanics.- 1. Principles of Wave Mechanics.- 1. Classical Mechanics of the Point Mass. Theory of Jacobi.- 2. Wave Propagation in an Isotropic Medium.- 3. Transition from Classical Mechanics to Wave Mechanics.- 4. General Equation for the Wave Mechanics of a Point Mass.- 5. Automatic Procedure for Obtaining the Wave Equation.- 2. Probabilistic Interpretation of Wave Mechanics.- 1. Interpretation of the ? Wave.- 2. Principle of Interference.- 3. Precise Statement of the Principle of Interference. Probability Fluid.- 4. The Uncertainty Relations of Heisenberg.- 5. The Principle of Spectral Decomposition (Born).- 6. New Ideas Resulting from the Preceding Conceptions.- 7. Return of Wave Mechanics to Classical Mechanics..- The Theorem of Ehrenfest. Group Velocity.- 3. Wave Mechanics of Systems of Particles.- 1. Old Dynamics of Systems of Point Masses.- 2. Wave Mechanics of Systems of Particles.- 3. Interpretation of Wave Mechanics for a System of Particles.- 4. General Formalism of Wave Mechanics.- 1. New Conception of the Quantities Attached to a Particle (or to a System).- 2. Eigenvalues and Eigenfunctions of a Linear Hermitian Operator.- 3. Continuous Spectrum of the Free-Particle Hamiltonian. Dirac's Delta Function.- 5. General Principles of the Probabilistic Interpretation of Wave Mechanics.- 1. General Ideas.- 2. The Algebraic Matrices and Their Properties.- 3. Operators and Matrices in Wave Mechanics.- 4. Mean Values and Dispersions in Wave Mechanics.- 5. First Integrals in Wave Mechanics.- 6. Angular Momentum in Wave Mechanics.- 6. Theory of the Commutation of Operators in Wave Mechanics.- 1. General Theorems.- 2. Corollaries of the Foregoing Theorems.- 3. Simultaneous Measurement of Two Quantities in Wave Mechanics.- 4. Examples of Quantities That Are Not Simultaneously Measurable. Distinction Between Two Kinds of Non-Commutation.- 7. Physical Impossibility of Simultaneously Measuring Canonically Conjugate Quantities.- 1. Necessity to Examine the Impossibility of Simultaneously and Precisely Measuring Two Canonically Conjugate Quantities.- 2. The Heisenberg Microscope.- 3. Measurement of the Speed of an Electron by Means of the Doppler Effect.- 4. Passage of a Particle through a Rectangular Aperture.- 5. Important Remark on the Measurement of Speed.- 6. The Case of Two Operators with a Nonzero Commutator.- 7. Bohr's Complementarity.- 8. Bohr's Calculation for Young's Slits.- 8. Precise Form of the Uncertainty Relations.- 1. Theorem About the Dispersion of Non-Commuting Quantities.- 2. Optimal Nature of the Gaussian Wave Packet.- 3. Comparison of the Theorem on Dispersions with the Qualitative Uncertainty Relations of Heisenberg (Pauli and Robertson).- 4. Various Considerations about Uncertainties. Sharp-edged Uncertainties.- 9. Heisenberg's Fourth Uncertainty Relation.- 1. The Absence of Symmetry between Space and Time in Wave Mechanics.- 2. Correct Formulation of the Fourth Uncertainty Relation.- 3. Illustration of the Preceding Definition.- 4. Various Remarks about the Fourth Uncertainty Relation.- 5. Method of Variation of Constants. Transition Probability.- 6. Transition Probabilities.- 7. Uncertainty Relations and Relativity Theory.- 8. Formulas of Mandelstam and Tamm.- 10. Examination of Some Difficult Points in Wave Mechanics.- 1. Reduction of the Probability Packet by Measurement.- 2. Impossibility of Discovering the Anterior State of a Measurement from its Posterior State. Effacement of Phases by Measurement.- 3. Possibility of Discovering the Past, Starting from a Measurement Made at a Given Instant (Postdiction).- 4. Interference of Probabilities.- 5. Some Consequences of the Disappearance of the Trajectory Concept.- 6. Discussions Concerning "Correlated" Systems.- 7. Complementary Remarks on the Einstein-Bohr Controversy.- Two (1951-1952) On the Probabilistic Interpretation of Wave Mechanics and Various Related Questions.- 11. Summary of Some General Concepts of Probability Calculus.- 1. Probability Laws for One Variable. Distribution Function.- 2. Probability Laws for Two Variables.- 3. Very Important Remark Concerning the Foregoing Results.- 12. Recalling the General Concepts of Wave Mechanics.- 1. The Interference Principle. Theory of the Pilot Wave.- 13. Introduction of the Characteristic Function into the Probability Formalism of Wave Mechanics.- 1. Characteristic Function for a Single Quantity.- 2. Characteristic Function for Two Commuting Quantities.- 3. Correlation Coefficient. Marginal Laws.- 4. General Theorems of Wave Mechanics Considered from the Characteristic-Function Point of View.- 5. Case of Two Noncommuting Quantities.- (a) Reminder About the Reduction of the Probability Packet by Measurement.- (b) Interference of Probabilities.- (c) The Distribution Function ?(x,?x) of Wigner and Bass.- (d) The Wigner-Bass Density ?(x,?x) and the Hydrodynamic Interpretation of Wave Mechanics.- (e) Yvon's Theory.- 14. Theory of Mixtures and von Neumann's Theory of Measurement.- 1. Mixtures and Pure Cases.- 2. Von Neumann's Statistical Matrix for a Pure Case.- 3. The Statistical Matrix for a Mixture of Pure Cases.- 4. Irreducibility of Pure Cases.- 5. Impossibility of Reducing the Laws of Wave Mechanics to a Hidden Determinism (von Neumann).- 15. Measurement Theory in Wave Mechanics.- 1. Generalities.- 2. Statistics of Two Interacting Systems.- 3. Correlation Coefficients in the Interaction between Two Quantum Systems.- 4. Measurement of a Quantity.- 5. Example of a Measuring Experiment.- 6. Diverse Remarks on Measurement.- 7. Thermodynamical Considerations (von Neumann).- 8. Reversible and Irreversible Evolutions.- 9. The Statistical Matrix P0.- 16. The Role of Time in Wave Mechanics.- 1. Retrodiction According to Costa de Beauregard.- 2. Special Role of Time in Quantum Mechanics. The Fourth Uncertainty Relation.- 3. Correct Statement of the Fourth Uncertainty Relation.- 4. The Fourth Uncertainty Relation and Perturbation Theory.- 5. The Operators H and (h/2?i)?/?t.- 6. Application of the Formalism of Arnous to the Operators Acting on Time.- 7. Multitemporal Formalism. Multiplicity Curves in Spacetime.- Works of Louis de Broglie.
Series Title: Fundamental theories of physics, v. 40.
Other Titles: Incertitudes d'Heisenberg et l'interprétation probabiliste de la mécanique ondulatoire.
Responsibility: by Louis de Broglie ; with a foreword by Asim Barut ; preface and supplementary notes by Georges Lochak ; translated by Alwyn van der Merwe.
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' Here is a truly essential book for scholars interested in the foundations of quantum physics. Heisenberg's Uncertainties is a unique work of landmark importance ... Heisenberg's Uncertainties and Read more...

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