Probability and Its Applications

Schrödinger Diffusion Processes

Authors: Aebi, Robert

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About this book

In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.

Table of contents (7 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-9027-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-7643-5386-5
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-9874-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Schrödinger Diffusion Processes
Authors
Series Title
Probability and Its Applications
Copyright
1996
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag Basel
eBook ISBN
978-3-0348-9027-4
DOI
10.1007/978-3-0348-9027-4
Hardcover ISBN
978-3-7643-5386-5
Softcover ISBN
978-3-0348-9874-4
Series ISSN
2297-0371
Edition Number
1
Number of Pages
186
Topics