The Principles of Newtonian and Quantum Mechanics: The Need for Planck’s Constant, h – eBook

The “The Principles of Newtonian and Quantum Mechanics: The Need for Planck’s Constant, h” 2nd edition of this PDF ebook deals, as the first, with the foundations of classical physics from the “symplectic” point of view, and of quantum mechanics from the “metaplectic” point of view. We have revised and augmented the topics studied in the 1st edition in the light of new results, and added many new sections. The Bohmian interpretation of quantum mechanics is discussed in good detail. Phase space quantization is achieved using the “principle of the symplectic camel”, which is a deep topological property of Hamiltonian flows. We introduce the notion of “quantum blob”, which can be viewed as the fundamental phase space unit. The mathematical tools developed in this ebook are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the “metatron” is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.