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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Schrödinger 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 tell 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.
Authors and Affiliations
Bibliographic Information
Book Title: Schrödinger Equations and Diffusion Theory
Authors: Masao Nagasawa
Series Title: Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-8568-3
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 1993
Hardcover ISBN: 978-3-7643-2875-7Published: 01 July 1993
Softcover ISBN: 978-3-0348-9684-9Published: 27 September 2012
eBook ISBN: 978-3-0348-8568-3Published: 06 December 2012
Series ISSN: 1017-0480
Series E-ISSN: 2296-4886
Edition Number: 1
Number of Pages: XII, 323