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OverviewSchrödinger Equations and Diffusion Theory addresses the question “What is the Schrödinger equation?” in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles. The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations. The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics. The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level. --- This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the profound mathematical properties of diffusion processes. (Mathematical Reviews) Full Product DetailsAuthor: Masao NagasawaPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: Reprint of the 1st edition 1993 by Birkhauser Verlag, Switzerland Dimensions: Width: 15.50cm , Height: 1.70cm , Length: 23.50cm Weight: 0.510kg ISBN: 9783034805599ISBN 10: 3034805594 Pages: 319 Publication Date: 14 December 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface.- I Introduction and Motivation.- II Diffusion Processes and their Transformations.- III Duality and Time Reversal of Diffusion Processes.- IV Equivalence of Diffusion and Schrödinger Equations.- V Variational Principle.- VI Diffusion Processes in q-Representation.- VII Segregation of a Population.- VIII The Schrödinger Equation can be a Boltzmann Equation.- IX Applications of the Statistical Model for Schrödinger Equations.- X Relative Entropy and Csiszar’s Projection.- XI Large Deviations.- XII Non-Linearity Induced by the Branching Property.- Appendix.- References.- Index.ReviewsAuthor InformationMasao Nagasawa is professor of mathematics at the University of Zurich, Switzerland. Tab Content 6Author Website:Countries AvailableAll regions |
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