An Alternative Approach to Wave Mechanics of A Particle at the Non-Relativistic Approximation
The mathematical theory of stochastic dynamic programming has cast a new light on the conceptual foundation of wave mechanics [1]. In this chapter we shall return to an illustration of that point of view, and more specifically to section 5 of the paper by
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INFORMATION COMPLEXITY AND CONTROL IN QUANTUM PHYSICS PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON MATHEMATICAL THEORY OF DYNAMICAL SYSTEMS AND MICROPHYSICS UDINE, SEPTEMBER 4-13, 1985
EDITED BY
A. BLAQUIERE, S. DINER, G. LOCHAK
Springer-Verlag
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Wien GmbH
Le spese di stampa di questo volume sono in parte coperte da contributi
del Consiglio Nazionale delle Ricerche.
This volume contains 20 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine
or similar means, and storage in data banks.
© 1987 by Springer-Verlag Wien Originally published by CISM, Udine in 1987.
ISBN 978-3-211-81992-0 ISBN 978-3-7091-2971-5 (eBook) DOI 10.1007/978-3-7091-2971-5
PREFACE
From September 4 to 13, 1985, a meeting took place at the International Centre for Mechanical Sciences (CISM), UdiRe, Italy. This was the fourth seminar in a series held since 1979, and devoted to dynamical systems, mechanics and microphysics. But with the first one, this was the second seminar almost exclusively devoted to problems of quantum physics and quantum theory. The other seminars, held in 1981 and 1983, were more specifically devoted to problems of mechanics under the subtitles : Geometry and mechanics, Control Theory and Mechanics. The general philosophy shared by the different organizers of these seminars was that microphysics could have some profit from interacting with the modern theory of dynamical systems and mathematical system theory. Such an idea was quite natural for people of the CISM, well aware of the huge modern developments of classical mechanics and dynamical system theory, often connected with the needs of technological progress in the field of automatic control and design of complex systems, the field of cybernetics. Such an idea was not and is not yet natural to quantum physicists. This is why the CISM asked the Fondation Louts de Broglie to organize an international Seminar on concepts and methods of cybernetics as they appear in quantum physics. This is the motivation for the title of this Seminar : Information, complexity and control in quantum physics. This seminar was not intended to be a conference on the problems of interpretation of quantum mechanics. Nevertheless a number of lectures and papers have a strong bearing on the basic questions in the foundations of quantum theory. Among the topics which could appear in such a conference were : Quantum probability, Quantum stochastic differential equations, Quantum chaos, Quantum stochastic processes, Open quantum systems and dissipation, Statistical theories for quantum physics, Quantum detection and estimation theory, Theory of measurements, Quantum information theory, Stochastic formulations of quantum mechanics, Quantum mechanics and control theory (Variational problems. Inverse problems), Quantum mechanical computers.
Many of these topics have been discussed from th
