Heisenberg’s Uncertainties and the Probabilistic Interpretation of Wave Mechanics : With Critical Notes of the Author

LOUIS DE BROGLIE AND THE SINGLE QUANTUM PARTICLE By A. O. Barut We have abundant evidence and testimony that Louis de Broglie deeply cared about the foundations, the meaning, and our understanding of quantum theory in general and of wave mechanics in particular. So, too, did Erwin Schrodinger, along with Einstein, Bohr, Dirac, and Heisenberg. For de Broglie and Schrodinger this preoccupation meant not simply the acceptance of a novel set of rules, but a constant struggle and a search for complete clarity about the way in which the new theory fits into the great classical traditions of an objective physical world view. We may call this a striving for "physical rigor," rigor in reasoning, or intellectual rigor. There is not only mathematical rigor inside an axiomatic system with which everybody agrees, but there is, and there should be, rigor also in our concepts and methods. To this kind of rigor belongs the unity, the economy and simplicity, and the consistency of physical theories; naturally along with as complete and as clear an understanding of phenomena as possible. No loose ends, no proliferation of poorly tested and phenomenological entities, no bending of logic and compromise, and no handwaiving arguments can be tolerated. Unfortunately this kind of rigor seems to be missing in today's forefront of fundamental physical theories, viz. , particle or high-energy physics. Front Matter....Pages i-xliv Front Matter....Pages 1-1 Principles of Wave Mechanics....Pages 3-14 Probabilistic Interpretation of Wave Mechanics....Pages 15-27 Wave Mechanics of Systems of Particles....Pages 28-33 General Formalism of Wave Mechanics....Pages 34-41 General Principles of the Probabilistic Interpretation of Wave Mechanics....Pages 42-54 Theory of the Commutation of Operators in Wave Mechanics....Pages 55-67 Physical Impossibility of Simultaneously Measuring Canonically Conjugate Quantities....Pages 68-84 Precise Form of the Uncertainty Relations....Pages 85-102 Heisenberg’s Fourth Uncertainty Relation....Pages 103-123 Examination of some Difficult Points in Wave Mechanics....Pages 124-150 Front Matter....Pages 151-151 Summary of some General Concepts of Probability Calculus....Pages 153-169 Recalling the General Concepts of Wave Mechanics....Pages 170-179 Introduction of the Characteristic Function into the Probability Formalism of Wave Mechanics....Pages 180-219 Theory of Mixtures and Von Neumann’s Theory of Measurement....Pages 220-237 Measurement Theory in Wave Mechanics....Pages 238-267 The Role of Time in Wave Mechanics....Pages 268-284 Back Matter....Pages 285-302