by Edward Nelson
Publisher: Princeton University Press 1985
Number of pages: 158
Stochastic mechanics is a description of quantum phenomena in classical probabilistic terms. This work contains a detailed account of the kinematics of diffusion processes, including diffusions on curved manifolds which are necessary for the treatment of spin in stochastic mechanics. The dynamical equations of the theory are derived from a variational principle, and interference, the asymptotics of free motion, bound states, statistics, and spin are described in classical terms. In addition to developing the formal mathematical aspects of the theory, the book contains discussion of possible physical causes of quantum fluctuations in terms of an interaction with a background field. The author gives a critical analysis of stochastic mechanics as a candidate for a realistic theory of physical processes, discussing measurement, local causality in the sense of Bell, and the failure of the theory in its present form to satisfy locality.
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by Charles G. Torre - Utah State University
This text will survey the foundations of quantum mechanics, basic techniques for its application to the real world, and a number of standard examples. It is assumed that you have already had a previous undergraduate course in quantum mechanics.
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Contents: Hamilton's Formalism of Classical Physics; State Vectors and Operators; The Position and Momentum Observables; Quantum Dynamics; The Harmonic Oscillator; Angular Momentum; Central Potential; Density Operator; Perturbation Theory; etc.
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A qualitative representation of microstates is established quite independently of the quantum mechanical mathematical formalism. The foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed.
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From a general study of the relations between models, meaning the set of variables with their mathematical properties, and the measures they represent, a new formalism is developed, which covers the scope of Quantum Mechanics.