Fundamental Theories of Physics

Quantum Theory from a Nonlinear Perspective

Riccati Equations in Fundamental Physics

Authors: Schuch, Dieter

  • A unique survey of the power of Riccati equations to describe reversible and irreversible processes in many areas of physics
  • Particular attention paid to non-linear versions of the Schrödinger equation
  • Reveals parallels in many seeming unrelated areas of physics, from quantum physics to fluid mechanics and cosmology
  • Author is a foremost expert with many years of experience in the field
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eBook $84.99
price for Mexico (gross)
  • ISBN 978-3-319-65594-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for Mexico
  • ISBN 978-3-319-65592-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

About the authors

Prof. Dr. Dieter Schuch
Institut fuer Theoretische Physik
Goethe-Universitaet Frankfurt am Main
Max-von-Laue-Str. 1
D-60438 Frankfurt am Main, Germany

Dieter Schuch received his Dr. Phil. nat. (1982) for Theoretical and Physical Chemistry at the J.W. Goethe-Universität Frankfurt am Main where he was also awarded his Habilitation for Theoretical Physics in 1992 and has been an Apl.-Professor since 2002. Guest Professorships and collaborations took him to IBM, New York, Toronto, Canada, Auckland, New Zealand, Nice, France, UNAM and CINVESTAV, Mexico, Granada, Spain, Salerno, Italy and the Frankfurt Institute for Advanced Studies (FIAS). Since 2009, he has undertaken the organization of the international conference series “Symmetries in Science”.

Table of contents (8 chapters)

  • Introduction

    Schuch, Dieter

    Pages 1-8

  • Time-Dependent Schrödinger Equation and Gaussian Wave Packets

    Schuch, Dieter

    Pages 9-67

  • Time-Independent Schrödinger and Riccati Equations

    Schuch, Dieter

    Pages 69-83

  • Dissipative Systems with Irreversible Dynamics

    Schuch, Dieter

    Pages 85-131

  • Irreversible Dynamics and Dissipative Energetics of Gaussian Wave Packet Solutions

    Schuch, Dieter

    Pages 133-177

Buy this book

eBook $84.99
price for Mexico (gross)
  • ISBN 978-3-319-65594-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for Mexico
  • ISBN 978-3-319-65592-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Theory from a Nonlinear Perspective
Book Subtitle
Riccati Equations in Fundamental Physics
Authors
Series Title
Fundamental Theories of Physics
Series Volume
191
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-65594-9
DOI
10.1007/978-3-319-65594-9
Hardcover ISBN
978-3-319-65592-5
Series ISSN
0168-1222
Edition Number
1
Number of Pages
XIV, 258
Number of Illustrations and Tables
8 b/w illustrations, 7 illustrations in colour
Topics