Schrödinger Equations and Diffusion Theory

Schrödinger Equations and Diffusion Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 333
Release :
ISBN-10 : 9783034805605
ISBN-13 : 3034805608
Rating : 4/5 (608 Downloads)

Book Synopsis Schrödinger Equations and Diffusion Theory by : Masao Nagasawa

Download or read book Schrödinger Equations and Diffusion Theory written by Masao Nagasawa and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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)​


Schrödinger Equations and Diffusion Theory Related Books

Schrödinger Equations and Diffusion Theory
Language: en
Pages: 333
Authors: Masao Nagasawa
Categories: Mathematics
Type: BOOK - Published: 2012-12-13 - Publisher: Springer Science & Business Media

GET EBOOK

Schrödinger Equations and Diffusion Theory addresses the question “What is the Schrödinger equation?” in terms of diffusion processes, and shows that the
Handbook of Brownian Motion
Language: en
Pages: 478
Authors: Andrei Borodin
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

GET EBOOK

There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The sec
Classes of Linear Operators
Language: en
Pages: 563
Authors: Israel Gohberg
Categories: Science
Type: BOOK - Published: 2013-03-09 - Publisher: Birkhäuser

GET EBOOK

These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the fi
Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory
Language: en
Pages: 153
Authors: Peter E. Zhidkov
Categories: Mathematics
Type: BOOK - Published: 2003-07-01 - Publisher: Springer

GET EBOOK

- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possess
Markov Processes and Quantum Theory
Language: en
Pages: 339
Authors: Masao Nagasawa
Categories: Computers
Type: BOOK - Published: 2021-06-23 - Publisher: Springer Nature

GET EBOOK

This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schrö