Advertisement

Schrödinger Equations and Diffusion Theory

  • Masao Nagasawa

Part of the Monographs in Mathematics book series (MMA, volume 86)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Masao Nagasawa
    Pages 1-12
  3. Masao Nagasawa
    Pages 115-138
  4. Masao Nagasawa
    Pages 139-162
  5. Masao Nagasawa
    Pages 163-206
  6. Masao Nagasawa
    Pages 239-252
  7. Masao Nagasawa
    Pages 253-260
  8. Back Matter
    Pages 281-323

About this book

Introduction

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.

Keywords

chaos diffusion process probability probability theory quantum mechanics

Authors and affiliations

  • Masao Nagasawa
    • 1
  1. 1.Institut für Angewandte MathematikUniversität ZürichZürichGermany

Bibliographic information