Quantum mechanics : principles, new perspectives, extensions and interpretation / Olavo Leopoldino da Silva Filho.

Format:

Book

Author/Creator:

Silva Filho, Olavo Leopoldino da, author.

Series:

Physics research and technology.

Physics Research and Technology

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

1 online resource (390 p.)

Edition:

Revised edition.

Place of Publication:

New York : Nova Publishers, 2016.

Summary:

The book Quantum Mechanics: Principles, New Perspectives, Extensions and Interpretation - Revised Edition deals with the foundations of Quantum Mechanics in a quite novel way. From his own published works throughout these last 20 years in prominent Journals, Prof. L.S.F. Olavo reconstructs Quantum Mechanics (as related to the Schr#65533;dinger equation) from the scratch, both in mathematical and interpretive ways. The picture that emerges is quite different from the one we get from other approaches. While the mainstream approach reinforces some unavoidable weirdness in the Quantum World, Prof. Olavo's interpretation presents Quantum Mechanics as quite an intuitive theory, using only the pedestrian notions of randomness, fluctuations and the companion notion of statistics. However, it is much more than another stochastic approach. Throughout the first part of the book, Prof. Olavo shows how the various roads to derive the Schr#65533;dinger equation can be reduced to his own mathematical construction: Feynman's path integral and the stochastic approach are but two of them. The book also brings about quite new results, such as the connection between Quantum Mechanics and the Central Limit Theorem and Langevin Equations (by means of which quantum phenomena can be easily simulated and make visualizable). All this is done taking recourse to only three axioms. This strategy gives the book an impressive power of synthesis in what respects the interpretation of the formalism. In fact, in the last part of the book, Prof. Olavo shows how some of the innumerous proposals for the interpretation of Quantum Mechanics, with some of their constructs, can help us making a rational reconstruction of a Quantum World without any weirdness whatsoever. In the second part, to remove some of the various obstacles to a Quantum Mechanics without weirdness, the book deals with the most prominent aspects and experiments of the Quantum, such as spin and the Stern-Gerlach experiment, the construction of operators and also Identical Particles. In the third part, the book presents a fully special and general relativistic extension of the formalism by just making the extension of the three postulates used throughout the first part. This book is intended to all those interested in the foundations of Quantum Mechanics.

Contents:

Contents; Preface; List of Tables; List of Figures; PART 1. PRINCIPLES; Historical Background - XIXth Century and Beyond; 1.1. The Early XIXth Century; 1.2. Waves and the Eletromagnetic Theory; 1.3. Matter and Atomism in the Xixth Century; 1.3.1. Chemical Atomism; 1.3.2. Physical Atomism; 1.4. Physics in the XXth Century; 1.5. The "Impossible" Reduction; 1.5.1. Early Discussions between Bohr and Einstein; 1.5.2. Three Roads to the Quantum; 1.5.3. The Beginning of the Battle on the Interpretation; 1.5.4. The Statistical Interpretation of Max Born

1.5.5. The formulation of the Uncertainty and Complementary Principles1.6. The Structure of the 1927 Interpretation: Reduction Revisited; The Characteristic Function Derivation; 2.1. The Axioms and the Formalism; 2.1.1. Heisenberg Dispersion Relations; 2.2. Quantization in Spherical Coordinates: An Example; 2.3. Quantization in Generalized Coordinates; 2.4. Generalization to Mathieu's Canonical Transformations; 2.5. Connection to Bohr-Sommerfeld Rules; 2.5.1. Corpuscular Interpretation of Bragg-Laue Diffraction; Another Approach to the Same Problem

2.5.2. Corpuscular Interpretation of Diffraction by an ApertureAlternative Explanation in Terms of Ewald Spheres; 2.6.3. Corpuscular Interpretation of Double Slit Interference; A Deeper Understanding of Interference and Diffraction Experiments; 2.6. Connections with Feynman's Path Integral Approach; The Entropy Derivation; 3.1. The Derivation; 3.2. Connections with the Characteristic Function Derivation; 3.3. Three-Dimensional Derivation; 3.4. The Phase-Space Probability Density Function; 3.4.1. The Stochastic Liouville Equation; 3.5. Average Values Calculated Upon Phase Space

4.5.1. The Formal Grounds for Electromagnetic Stochastic Behavior4.5.2. Corpuscular Interpretation of the Tunnel Effect; Quantum Mechanics and the Central Limit Theorem; 5.1. The Central Limit Theorem for One Random Variable; 5.2. Phase Space Derivation; 5.3. Connection with The Characteristic Function Derivation; 5.4. The CLT Derivation of the Schrödinger Equation; 5.5. Ensemble and Single Systems Revisited; 5.6. Ontological Duality As a False Problem; 5.6.1. The Epistemological Interpretation of Heisenberg Relations; 5.7. The Dispersion Relations

5.7.1. What Do we Need Quantum Mechanics for?

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-63485-574-4